Answers
Given:
The diagram of a cone.
To find:
The lateral area, surface area and volume of the cone.
Solution:
From the given diagram, we get
Radius of the cone = 6
Slant height of the cone = 10
Suppose [tex]h[/tex] be the height of the cone.
According to Pythagoras theorem:
[tex]hypotenuse^2=Perpendicular^2+Base^2[/tex]
Using the Pythagoras theorem, we get
[tex]10^2=(6)^2+h^2[/tex]
[tex]100=36+h^2[/tex]
[tex]100-36=h^2[/tex]
[tex]64=h^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{64}=h[/tex]
[tex]8=h[/tex]
The lateral area of a cone is:
[tex]A_L=\pi rl[/tex]
[tex]A_L=\pi (6)(8)[/tex]
[tex]A_L=48\pi[/tex]
The surface area of a cone is:
[tex]A_S=\pi rl+\pi r^2[/tex]
[tex]A_S=\pi (6)(8)+\pi (6)^2[/tex]
[tex]A_S=48\pi +36\pi[/tex]
[tex]A_S=84\pi[/tex]
Volume of cone is:
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
[tex]V=\dfrac{1}{3}\pi (6)^2(8)[/tex]
[tex]V=\dfrac{288}{3}\pi [/tex]
[tex]V=96\pi [/tex]
Hence, the lateral area of a cone is [tex]48\pi[/tex] sq. units, the surface area of a cone is [tex]84\pi[/tex] sq. units and the volume of the cone is [tex]96\pi[/tex] cubic units.
Related Questions
That is, what is the 142nd odd number?
Answers
Answer and step-by-step explanation:
I believe it is 287. I am not entirely sure, but I believe that is the answer.
For which color is the difference between the theorectical probability and experimental probability greatest?
A.
Brown; The experimental probability is 19.52%, and the theoretical probability is 25%.
B.
Orange; The experimental probability is 18.9%, and the theoretical probability is 15%.
C.
Yellow; The experimental probability is 16.96%, and the theoretical probability is 20%.
D.
Green; The experimental probability is 22.7%, and the theoretical probability is 15%.
Answers
Answer:
The answer is D. Green; The experimental probability is 22.7%, and the theoretical probability is 15%.
A company estimates that 0.1% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $350. If they offer a 2 year extended warranty for $28, what is the company's expected value of each warranty sold?
Answers
Answer:
The expected gain per warranty is $27.65, crazy stuff
Step-by-step explanation:
If the estimate is right, there is a 0.1% probability for each extended warranty that the company has to shell out $350 (we disregard the situation where the replacement fails too, because there is no info that lets us deal with that).
This brings us to cost for the company equal to 0.1%*$350 per warranty sold.
0.1%*$350 = 0.001*$350 = $0.35
And the company gets $28 for each warranty sold, hence they earn
$28 - $0.35 = $27.65
on average.
what is the percentage of 750ml of 2 litres
Answers
Answer: 75%
Step-by-step explanation:
We convert 2 litres into 1000ml which leaves us with:
750/1000 x 100 = 75%
Answer:
37.5%
Step-by-step explanation:
as a percentage it is (750 * 100)/2000
= 750 / 20
= 75/2
= 37.5%.
Evaluate 79-4*6+12/3
Answers
Answer:
59 (the answer should have a positive sign.)Step-by-step explanation:
To solve this problem, you have to solve with order of operations.
Order of operations stands for:
PEMDAS
Parentheses
Exponents
Multiply
Divide
Add
Subtract
Do multiply.
79-4*6+12/3
4*6=24
Rewrite the problem down.
79-24+12/3
Divide.
12/3=4
79-24+4
Add and subtract.
79-24=55
55+4
55+4=59
[tex]\sf\boxed{59}[/tex]
As a result, the final answer is 59.
Given f(x)=2x^2-5x+kf(x)=2x2−5x+k, and the remainder when f(x) is divided by x-1x−1 is -22−22, then what is the value of k?
Answers
Answer:
k=20
remainder=34
Step-by-step explanation:
What is the answer to this pls help
Answers
Step-by-step explanation:
Circumference is 6π = 18.85 in
if you were looking for area
9π = 28.27 in
Answer:
18.85 would be your answer sorry I was so late
Step-by-step explanation:
mean of 500 with a standard deviation of 100. What is the probability that a randomly selected score lies between 500 to 700?
Answers
Answer: 99.7% of data will fall within 3 standard deviations of the mean. The mean is 500 and the standard deviation is 100. ... Since we are only concerned with the scores from 500 to 700, we only want the half that is greater than the mean: 95/2 = 47.5%, or 0.475.:
Step-by-step explanation:
At a certain university, the average attendance at basketball games has been 3125. Due to the dismal showing of the team this year, the attendance for the first 9 games has averaged only 2915 with a standard deviation of 585. The athletic director claims that the attendance is the same as last year. What is the test statistic needed to evaluate the claim
Answers
Answer:
The test statistic needed to evaluate the claim is t = -1.08.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected value of the mean, s is the standard deviation of the sample and n is the size of the sample.
At a certain university, the average attendance at basketball games has been 3125. The athletic director claims that the attendance is the same as last year.
This means that [tex]\mu = 3125[/tex]
Due to the dismal showing of the team this year, the attendance for the first 9 games has averaged only 2915 with a standard deviation of 585.
This means that [tex]n = 9, X = 2915, s = 585[/tex]
What is the test statistic needed to evaluate the claim?
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{2915 - 3125}{\frac{585}{\sqrt{9}}}[/tex]
[tex]t = -1.08[/tex]
The test statistic needed to evaluate the claim is t = -1.08.
Find the decimal number halfway between the following decimal number 0.7 and 0.5
Answers
Answer:
0.6?
Step-by-step explanation:
confused by the question but thats the middle decimal..
Please help my little brother!!!!
Answers
Answer:
H
Step-by-step explanation:
Answer:
H. 3.9
Step-by-step explanation:
5.6 - 1.7 = 3.9
Can the theoretical probability of the cup landing on its side be calculated based on the information given?
Answers
Answer:
If given enough information yes
Step-by-step explanation:
If you were given the weight and the distibution of the weight and the elasticity of the cup, as well as the trajectory of the cup and the force it was thrown at, and the proportions of the cup, its shape, where it's landing, etc. You could give a definitive probability. For example, If there is more weight at the bottom of the cup it might be less probable to land on it's side
Under her cell phone plan, Savannah pays a flat cost of $37.50 per month and $3 per
gigabyte. She wants to keep her bill at $51.90 per month. Which equation or tape
diagram could be used to represent the context if g represents the number of
gigabytes of data Savannah can use while staying within her budget?
Answers
Answer:
(51.90 - 37.50) / 3 = G
14.40 / 3 = G
4.8 = G
Savannah will be able to use 4 gigabytes to stay within her budget.
Step-by-step explanation:
Given that under her cell phone plan, Savannah pays a flat cost of $ 37.50 per month and $ 3 per gigabyte, and she wants to keep her bill at $ 51.90 per month, to determine which equation or tape diagram could be used to represent the context if g represents the number of gigabytes of data Savannah can use while staying within her budget, the following calculation should be performed:
(51.90 - 37.50) / 3 = G
14.40 / 3 = G
4.8 = G
Therefore, Savannah will be able to use 4 gigabytes to stay within her budget.
Find the measures of the numbered angles in each kite.
Answers
Answer:
1 = 20°
2 = 90°
3 = 70°
4 = 55°
Two traffic lights operate independently. Your probability of being stopped at the first one is 0.4 and your probability of being stopped at the second one is 0.7. The probability at being stopped at the first light and second light is 0.3. What is your probability of being stopped at the first light or second light?Make sure to show your work. NEED HELP ASAP. The correct answer was .8 I just don't know how. Thank you.
Answers
Answer:
0.54 or 54%
Step-by-step explanation:
P( 1st but not second) = P(1st) - P(1st and Second) = 0.4 - 0.28 = 0.12 = 12%
P( 2nd but not first) = P(2nd) - P(1st and Second) = 0.7 - 0.28 = 0.42 = 42%
Probability of 1 of them (exactly one) = P( 1st but not second) + P( 2nd but not first) = 0.12 (12%) + 0.42 (42%) = 0.54 or also 54%.
Hope this helps!
pls it's due today.
Miguel cuts a square with 5 inch sides out of a circle with a 12 inch diameter. Find the area of the remaing piece of the nearest tenth. Show all work
Answers
Answer:
[tex]31 \times \frac{52}{24x6} [/tex]
Donut $2.50
Cupcake $4.25
Ice cream $3.80
I need help finding the equation
Answers
plsss help me and I will mark u as brainliest plssss help
Answers
Answer:
In my sketch the angle between their flights is 135°
So wouldn't we just have the cosine law??
Step-by-step explanation:
x^2 = 120^2 + 150^2 - 2(120)(150)cos135°
carry on, take care with the cos135, since it will be negative
Which one of the following is an equation?
O 3m + 2
3m
2
3m +2 = 11
Answers
Answer:
3m+2=11
Step-by-step explanation:
Because equation is joined with equal sign
find the area of the shaded region to the nearest tenth
Answers
Answer:
Area of shaded region = 13.07 unit² (Approx.)
Step-by-step explanation:
Given:
Given shaded region is a segment
Radius of circle = 12
Given angle = 60°
Find:
Area of shaded region
Computation:
Area of shaded region = Area of segment
Area of segment = (θ/360)(π)(r²) - (1/2)(sinθ)(r²)
Area of segment = (60/360)(22/7)(12²) - (1/2)(sin60)(12²)
Area of segment = (0.1667)(3.14)(144) - (0.5)(0.866)(144)
Area of segment = (75.42) - (62.35)
Area of segment = 13.07 unit²
Area of shaded region = 13.07 unit² (Approx.)
What is the surface area of a cylinder that is 5 centimeters high and has a diameter of 1.5 centimeters?
7.51 cm2
8.6251 cm2
o
10.5 cm
19.551 cm2
Answers
Answer: SA≈27.1.
The formula is SA=2πrh+2πr2.
The radius is 0.75 since 1.5 divided by 2=0.75.
Plug it in.
Please help on both questions. I would appreciate it.
Answers
Answer:
first one is 4.5 second one is 45
Step-by-step explanation:
Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, square root of (6) as zeros. Find the other zero
Answers
Find the value of x and the measure of the angle labeled 3X°. 27° O A. x = 15; angle measure is 45°. OB. X = 9; angle measure is 27º. O c. x = 15; angle measure is 27°. D. X = 9; angle measure is 45°
Answers
Answer:
B. x=9, angle measure is 27 .
Step-by-step explanation:
sol :-
72 - 45 = 27
or 3x and 27° are the vertically opposite angles.
so :-
3x = 27
then : x = 27÷3
X= 9
The roof pictured below has a rise of 10 feet and a run of 15 feet.
Run = 15 feet
Rise = 10 feet
-
What is its slope?
Answers
The slope of the considered roof which has a rise of 10 feet and a run of 15 feet is 2/3
How to find the slope?Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increament in the run.
Thus, we get:
Slope = rise/ run
For this case, we're specified that:
The rise in roof = 10 ft and the run of 15 ft.
Thus, we get:
Slope = rise / run = 10/15 = [tex]\dfrac{5 \times 2}{5 \times 3} = \dfrac{2}{3}[/tex]
Thus, the slope of the considered roof which has a rise of 10 feet and a run of 15 feet is 2/3
Learn more about slope here:
https://brainly.com/question/2503591
use the Pythagorean theorem to find the distance between (-5,2) and (10,10)
Answers
D^2 = (x2-x1)^2 + (y2-y1)^2
D =sqrt((10+5)^2 + (10-2)^2)
D P SQRT(15^2 + 8^2)
D = sqrt(225 +64)
D= sqrt(289)
D = 17
The distance is 17
11r + 7s written form plz i need help
Answers
Answer:
eleven r plus seven s
Step-by-step explanation:
thats the written form
una escuela debe transportar 200 estudiantes
Answers
Answer: a school must transport 200 students
Step-by-step explanation:
I need help. Please help
Answers
Answer:
150 degrees
Step-by-step explanation:
Answer:
You need 180 degrees for a triangle so, you subtract 150 from 180.
You get 30 degrees.
Then, you subtract 30 from 180 in order to find the degree of x.
The number for x is: 150 degrees
I hope this helps ! :)
Step-by-step explanation:
a rectangle has a perimeter of 6 feet .choose all possible dimensions
Answers
Options aren't given in the question. However a concise explanation will be given.
Answer:
Length = 1 ; width = 2 and vice versa
Length = 0.5 ; width = 2.5 and vice versa
Step-by-step explanation:
The perimeter of a rectangle is obtained using the formular :
Perimeter = 2(length + Width)
Hence the sum of the length and width of the rectangle multiplied by 2 should give 6
Hence, possible dimension will. Include :
A dimension whereby the sum of length and width gives 3
Length = 1 ; width = 2 and vice versa
Length = 0.5 ; width = 2.5 and vice versa
These are possible dimension of the rectangle which has a perimeter of 6