Answer:
60%
Step-by-step explanation:
We need convert 3/5 into a percent in order to find the answer.
We can convert by first dividing 3 by 5 to find the decimal value.
3/5= .6
Now we need to multiply by 100 to make it a percentage
.6 x 100= 60
60%
Use the line of best fit to determine the x-value when the y- value is 190
Answer:
A. 9
Step-by-step explanation:
Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.
Thus,
A.9 is the correct answer.
Hope this helps :)
Answer:
A. 9
Step-by-step explanation:
A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.
Simplify the expression.(4+2i)-(1-i)
ANSWER :
6i - (1-i)
Step - by - step explanation:
( 4 + 2i ) - ( 1 - i )
( 4 + 2 × i) - ( 1 - i )
( 6× i ) - ( 1 - i )
= 6i- (1-i)
Hope this helps and pls mark as brainliest :)
Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.
Answer:
In 10 years she'll have approximately $21865.4 in her account.
Step-by-step explanation:
When an amount is compounded continuously its value over time is given by the following expression:
[tex]v(t) = v(0)*e^{rt}[/tex]
Applying data from the problem gives us:
[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]
In 10 years she'll have approximately $21865.4 in her account.
Answer:
21,865.43
previous answer left out the last digit
Step-by-step explanation:
Use Bayes' theorem to find the indicated probability 5.8% of a population is infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
a. 0.905
b. 0.585
c. 0.038
d. 0.475
Answer:
b. 0.585
Step-by-step explanation:
According to Bayes' theorem:
[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]
Let A = Person is infected, and B = Person tested positive. Then:
P(B|A) = 93.9%
P(A) = 5.8%
P(B) = P(infected and positive) + P(not infected and positive)
[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]
Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:
[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]
The probability is 0.585.
Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years
Answer:
The value of annuity is [tex]P_v = \$ 7929.9[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 250[/tex]
The interest rate is [tex]r = 5\% = 0.05[/tex]
Frequency at which it occurs in a year is n = 4 (quarterly )
The number of years is [tex]t = 10 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)
substituting values
[tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]
[tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]
[tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]
[tex]P_v = \$ 7929.9[/tex]
pleaseeee helppppp meeeee pleaseeeeee
Answer:
(28/33+28 ) *100
Step-by-step explanation:
(28/33+28 ) *100
(28/61)*100
Answer:
it's 2
Step-by-step explanation:
I did it before
The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
At noon a passenger train leaves the Dupont Railway station and travels due east for 2 hours. At 12:45 pm the same day a second passenger train leaves the same railway station and travels due west for 1 hour and 15 minutes at a speed 10 kilometers per hour slower than the first passenger train. At 2pm the two trains were 215 kilometers apart. How fast had each train been traveling
Answer:
The speed of the first train is 70 km/hr
The speed of the second train is 60 km/hr
Step-by-step explanation:
For the first train:
Travel time = 2 hours
The speed = ?
we designate the speed as V
For the second train:
The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)
speed = 10 km/hr slower than that of the first train, we can then say
the speed = V - 10
The total distance traveled by both trains in the opposite direction of one another is 215 km
we can put this problem into an equation involving the distance covered by the trains.
we know that distance = speed x time
the distance traveled by the first train will be
==> 2 hrs x V = 2V
the distance traveled by the second train will be
==> 1.25 hrs x (V - 10) = 1.25(V - 10)
Equating the above distances to the total distance between the trains, we'll have
2V + 1.25(V - 10) = 215
2V + 1.25V - 12.5 = 215
3.25V = 215 + 12.5
3.25V = 227.5
V = 227.5/3.25 = 70 km/hr this is the speed of the first train
Recall that the speed of the second train is 10 km/hr slower, therefore
speed of the second train = 70 - 10 = 60 km/hr
The speed of the trains are 70km/hr and 60km/hr respectively.
The distance of the first train will be represented by: = 2 × D = 2D
The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).
Based on the information given in the question, the equation to solve the question will be:
2D + 1.25(D - 10) = 215
Collect like terms
2D + 1.25D - 12.5 = 215
3.25D = 215 + 12.5
3.25D = 227.5
D = 227.5/3.25
D = 70km/hour
The speed of the second train will be:
= 70 - 10 = 60km per hour.
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Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How much blue paint does he need?
Answer:
Blue paint=21 ounces
Step-by-step explanation:
3/4 cup=6 ounces
1 cup=8 ounces
3/4 cup of blue paint=6 ounces of blue paint
1 cup of white paint= 8 ounces of white paint
Ava has 28 ounces of white paint
Find the required blue paint
Let the required blue paint=x
Blue paint ratio white paint
6:8=x:28
6/8=x/28
Cross product
6(28)=x(8)
168=8x
x=168/8
x=21 ounces
Which table represents the inverse of the function defined above?
Hello!
Answer:
Table B.
Step-by-step explanation:
An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:
We can use points on the table:
[tex]f(x)[/tex] = (7, 21)
The inverse of this function would 7 as its y value, and 21 as its x value:
[tex]f^{-1} (x)[/tex] = (21, 7)
The only table shown that correctly shows this relationship is table B.
The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time. When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year. By how much does the machine depreciate during the fifth year
Answer: The machine depreciates during the fifth year by $4000.
Step-by-step explanation:
Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.
When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.
Then, the machine depreciates A(x) during the fifth year as
[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]
Hence, the machine depreciates during the fifth year by $4000.
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced?
Answer:
The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.
Determine the measure of the unknown variables.
Answer:
75
Step-by-step explanation:
x = 75°
yes x = 75°(OPPOSITE ANGLES ARE EQUAL)
..
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the trigonometric ratios with their values based on the triangle shown in the diagram.
Answer:
A-2, B-DNE*, C-3, D-DNE, E-4, F-1
---------------------
The first attachment shows the solutions to A and C.
The second attachment shows the solutions to E and F.
There are no real number solutions to systems B and D.
_____
In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.
A.
(3-x) +12 = x^2 +x
15 = x^2 + 2x
16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root
±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A
__
B.
(x -1) -15 = x^2 +4x
-16 = x^2 +3x
-13.75 = x^2 +3x +2.25 = (x +1.5)^2
roots are complex: -1.5 ±i√13.75
__
C.
(1-2x) +5 = x^2 -3x
6 = x^2 -x
6.25 = x^2 -x + .25 = (x -.5)^2
±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C
__
remaining problems are done in a similar way.
_____
* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.
---------------------
Hope this helps!
Brainliest would be great!
---------------------
With all care,
07x12!
A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is $6.00 for adults and $3.00 for students. However, this situation has two constraints: The theater can hold no more than 240 people and for every two adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of money?
Answer:
160 adults and 80 students
Step-by-step explanation:
With the information from the exercise we have the following system of equations:
Let x = number of students; y = number of adults
I want to maximize the following:
z = 3 * x + 6 * y
But with the following constraints
x + y = 240
y / 2 <= x
As the value is higher for adults, it is best to sell as much as possible for adults.
So let's solve the system of equations like this:
y / 2 + y = 240
3/2 * y = 240
y = 240 * 2/3
y = 160
Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.
A city's population is currently 50,000. If the population doubles every 70 years, what will the population be 280 years from now?
Answer:
200,000
Step-by-step explanation:
The current population: 50,000
Doubling time:70
Population after 280 years=?
280/70=4
50,000*4=200,000
Hope this helps ;) ❤❤❤
Answer: 800,000
Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
A rectangle is to be inscribed in a right triangle having sides of length 6 in, 8 in, and 10 in. Find the dimensions of the rectangle with greatest area assuming the rectangle is positioned as in Figure 1. Figure1
Answer: width = 2.4 in, length = 5
Step-by-step explanation:
The max area of a right triangle is half the area of the original triangle.
Area of the triangle = (6 x 8)/2 = 24
--> area of rectangle = 24 ÷ 2 = 12
Next, let's find the dimensions.
The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.
length = 10 ÷ 2 = 5
Use the area formula to find the width:
A = length x width
12 = 5 w
12/5 = w
2.4 = w
The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.
Let the length and width of the rectangle be x and y.
Then Area of the rectangle = xy
Now, from the triangle we can conclude that
[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]
Put the value of y in Area we get
[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]
Differentiating it w.r.t x we get
[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]
Put A'(x)=0 for maximum /minimum value
[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]
Now, [tex]A''(3)=-\frac{8}{3} <0[/tex]
Therefore the area of the rectangle is maximum for x=3 inch
Now,
[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]
Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.
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i
dont
get
this
help
rn
Answer:
6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.
Step-by-step explanation:
Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.
If ABC~DEF and the scale factor from ABC to DEF is 3/4, what is the length of DF?
Answer:
the length of DF = 3/4 AC
see below for explanation
Step-by-step explanation:
ABC is said to be approximately equal to DEF
The scale factor from ABC to DEF = 3/4
From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.
We can deduce from the question, ΔABC was dilated to form ΔDEF
In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.
In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :
AB, BC and AC
ΔDEF has 3 sides : DE, EF and DF
If AB corresponds to DE
BC corresponds to EF
AC corresponds to DF
Then:
length DE = scale factor × AB = 3/4 AB
length EF = scale factor × BC = 3/4 BC
length DF = scale factor × AC = 3/4 AC
Therefore, the length of DF = 3/4 AC
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. VIEW FILE ATTACHED
Answer: see below
Step-by-step explanation:
[tex]P(x)=\dfrac{2}{3x-1}\qquad \qquad Q(x)=\dfrac{6}{-3x+2}\\[/tex]
P(x) ÷ Q(x)
[tex]\dfrac{2}{3x-1}\div \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\times \dfrac{-3x+2}{6}\\\\\\=\large\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]
P(x) + Q(x)
[tex]\dfrac{2}{3x-1}+ \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)+ \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)+6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4+18x-6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{12x-2}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{2(6x-1)}{(3x-1)(-3x+2)}}[/tex]
P(x) - Q(x)
[tex]\dfrac{2}{3x-1}- \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)- \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)-6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4-18x+6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-24x+10}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{-2(12x-5)}{(3x-1)(-3x+2)}}[/tex]
P(x) · Q(x)
[tex]\dfrac{2}{3x-1}\times \dfrac{6}{-3x+2}\\\\\\=\large\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
Con proceso por favor
Answer:se
Step-by-step explanation:
Assume that IQ scores are normally distributed, with a standard deviation of 16 points and a mean of 100 points. If 60 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points
Answer:
The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
The number of users on a website has grown exponentially since its launch. After 1 month, there were 120 users. After 4 months, there were 960 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
f(x) = 60(2)ˣ
Step-by-step explanation:
f(x) = a(b)ˣ
After one month:
120 = a(b)¹
After four months:
960 = a(b)⁴
Divide the second equation by the first:
8 = b³
b = 2
Plug into either equation and find a.
120 = a(2)¹
a = 60
Therefore, f(x) = 60(2)ˣ.
In the diagram of RST, which term describes point U?
A.
Circumcenter
B.
Centroid
C.
Incenter
D.
Orthocenter
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The correct option is C, Incenter.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In a triangle, the point at which all the angle bisectors of the triangle meet is known as the Incenter.
Since In ΔRST, all the angles are bisected by the angle bisector, and the point at which all the angle bisectors meet is represented by U. Thus, it can be concluded that the point U represents the incenter of the triangle.
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PLLZZZZ help me find x you are AWSOME!! I need this ASAP
Answer:
27°
Step-by-step explanation:
D is 72° because it alternates with B, alternate angles are equal.
2x+72°+2x= 180° because it is a straight line.
4x+72°=180°
4x=108°
x=27°
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
Answer:A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.
Step-by-step explanation:
The cylinder is given by A = pi/4 the volume of the prism or π/4 x (4r²h) or π x r² x h
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Area circle is A = πr²
Area square with side s = s²
The side of the square is equal to the diameter of the circle
Area square = D²
A diameter of square is always twice the radius
Area square = (2r)² = 2²r² = 4r²
So , on simplifying , we get
Area circle/Area square = (πr²)/(4r²)
Area circle/Area square = π/4
Now , The volume Prism = Area Square x h
Volume Prism = 4r²h
Volume of Cylinder= Area Circle x h
Volume of Cylinder = π x r² x h
So , Volume Cylinder/Volume Prism = π x r² x h/4r² x h
Volume of Cylinder/Volume of Prism = π/4
Volume of Cylinder = π/4 x Volume Prism
And , The volume of Cylinder = π/4 x (4r²h)
Hence , the volume of cylinder is V = π/4 x (4r²h)
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