A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythagoras' Theorem thank you)

Answers

Answer 1

Answer:

[tex] \displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3} [/tex]

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

[tex]\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s[/tex]

where B stands for Base area

and P for Base Parimeter

so

[tex] \sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s[/tex]

now we need our algebraic skills to figure out s

simplify parentheses:

[tex] \sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144[/tex]

reduce fraction:

[tex] \sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144[/tex]

simplify multiplication:

[tex] \displaystyle \: 16s + 64 = 144[/tex]

cancel 64 from both sides;

[tex] \displaystyle \: 16s = 80[/tex]

divide both sides by 16:

[tex] \displaystyle \: \therefore \: s = 5[/tex]

now we'll use Pythagoras theorem to figure out height

according to the theorem

[tex] \displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2} [/tex]

substitute the value of l and s:

[tex] \displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2} [/tex]

simplify parentheses:

[tex] \displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2} [/tex]

simplify squares:

[tex] \displaystyle \: {h}^{2} + 16 = 25[/tex]

cancel 16 from both sides:

[tex] \displaystyle \: {h}^{2} = 9[/tex]

square root both sides:

[tex] \displaystyle \: \therefore \: {h}^{} = 3[/tex]

recall the formula of a square pyramid

[tex]\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h[/tex]

where A stands for Base area (l²)

substitute the value of h and l:

[tex] \sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3[/tex]

simplify multiplication:

[tex] \sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3[/tex]

reduce fraction:

[tex] \sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}[/tex]

hence,

[tex] \sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3} [/tex]


Related Questions

help please lolololololololo

Answers

Answer:

C. x= 3 ; angle measure is 48°

Step-by-step explanation:

the two angles created by the X are the equal, so to make 16 equal to 48 we multiply by 3

hope this helps chu <3

In PQR the measure of R=90 the measure of P=62 and RP=8.6 find the length of QR to the nearest tenth of a foot.

Answers

Answer:

QR = 4.6 ft

Step-by-step explanation:

By applying tangent rule in the given triangle PQR,

tan(62°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

             = [tex]\frac{8.6}{QR}[/tex]

QR = [tex]\frac{8.6}{\text{tan}(62)}[/tex]

QR = 4.573

QR ≈ 4.6 ft

a truck sits on the platform of a vehicle lift. Two moving arms raise the platform until a mechanic can fit underneath. Why will the truck always be parallel to the ground as it is lifted?

Answers

Answer:

Step-by-step explanation:Because many objects are not regularly shaped their volume cannot be determined using a volume formula. The volume of these objects can be found by water displacement. A volume of water sufficient to cover the object is placed in a graduated cylinder and the volume read. The object is added to the cylinder and the volume read again. The difference between the two volumes is the volume of the object. This method is demonstrated using the same battery used above.

A triangle has sides of length 2 cm and 12 cm. What can you say about the length of the third​ side?

Answers

Answer:

The third side must be between 10cm and 14 cm

Step-by-step explanation:

Let the third side be x

Triangle inequality theorem: sum of the length of any two sides must be greater than the third side length:

2 + 12 > x ⇒ x < 142 + x > 12 ⇒ x > 10x + 12 > 2 ⇒ x > -10, we change it to x > 0 as it should be a positive number

Combined together we have:

10 < x < 14

The third side must be between 10cm and 14 cm

Help? ...................​

Answers

Answer:

7) C.it wil change direction

8) B.time,position,and velocity

9) A.-6km/hr

10) C.2km/hr

11) D.when an object changes its direction

12) B. Direction

What is the median of these scores,
98,82,100,84?

Answers

Answer:

the median is 91

Step-by-step explanation:

have a good day

Solve the equation.
m2-14 – 29

Answers

Answer:

m = 15

Step-by-step explanation:

m + 14 = 29

Subtract the 14...

m = 15

I hope this helps :)

Answer:

m = 15

Step-by-step explanation:

()) A rectangular piece of paper has a perimeter of 22 inches and an area of 28 square
inches. What are the dimensions of the paper?

Answers

Given:

Perimeter of a rectangular paper = 22 inches.

Area of the rectangular paper = 28 square inches.

To find:

The dimensions of the rectangular paper.

Solution:

Let l be the length and w be the width of the rectangular paper.

Perimeter of a rectangle is:

[tex]P=2(l+w)[/tex]

Perimeter of a rectangular paper is 22 inches.

[tex]2(l+w)=22[/tex]

[tex]l+w=\dfrac{22}{2}[/tex]

[tex]l=11-w[/tex]                      ...(i)

Area of a rectangle is:

[tex]A=lw[/tex]

Area of the rectangular paper is 28 square inches.

[tex]28=lw[/tex]

Using (i), we get

[tex]28=(11-w)w[/tex]

[tex]28=11w-w^2[/tex]

[tex]w^2-11w+28=0[/tex]

Splitting the middle term, we get

[tex]w^2-7w-4w+28=0[/tex]

[tex]w(w-7)-4(w-7)=0[/tex]

[tex](w-7)(w-4)=0[/tex]

Using zero product property, we get

[tex](w-7)=0\text{ and }(w-4)=0[/tex]

[tex]w=7\text{ and }w=4[/tex]

If [tex]w=7[/tex], then by using (i)

[tex]l=11-7[/tex]

[tex]l=4[/tex]

If [tex]w=4[/tex], then by using (i)

[tex]l=11-4[/tex]

[tex]l=7[/tex]

Therefore, the dimensions of the paper are either [tex]7\times 4[/tex] or [tex]4\times 7[/tex].

tell me if i did these correctly and i will mark you brainiest

Answers

Answer:

You only got 7, 8, and 9 wrong

Step-by-step explanation:

it said convert to percents not fractions. Number 7 is 35%, number 8 is 80%, and number 9 is 126%

someone help with number 2. (it’s algebra 1)

Answers

Answer:

98 followers

Step-by-step explanation:

Because 82(1.045)^4 is equal to 97.7865252512 which is 98 when you round it to the whole number...

GOOD LUCK

Give examples of numbers that you would multiply by 3 to get an answer that is greater than 3, equal to 3, or less than 3

Answers

Answer:

1. 3 x 3 = 9

2. 3 x 1 =3

3. 3 x 0.4 = 1.2

Step-by-step explanation: Hope this helps :)

Help fast please i need it​

Answers

Answer:

420

Step-by-step explanation:

Answer:

420

Step-by-step explanation:

vnhfuurrttjnnnnnbh

Find the circumference of the circle. Use 3.14 for pi round the nearest hundredth rig necessary. 30 in the circumference of the circle is abt something in

Answers

Answer:

C=2 [tex]\pi[/tex] r

Step-by-step explanation:

Which point is a solution to the inequality shown in this graph? (0,4) (-3,0)

Answers

Answer: (-3,0)

Hope this helps :_)

Determine if the figures are similar. If they are, what is the scale factor from the first figure to the second figure?

Answers

Answer:

The scale factor is [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Yes the figures are similar to each other. The ratio of their linear measurements is in uniform ration

The ration of radius of large cylinder (R) to that of the smaller cylinder (r) is

[tex]\frac{18}{12} \\\frac{3}{2}[/tex]

Like wise the ration of height of large cylinder (H) to that of the smaller cylinder (h) is

[tex]\frac{30}{20} \\\frac{3}{2}[/tex]

The scale factor is [tex]\frac{3}{2}[/tex]

A technology company claims that 13% of customers who call the help desk cannot log in because they have their keyboard on caps lock, which blocks the log in process due to password case sensitivity. Brian, a help desk worker at this company, thinks this proportion is higher. The 95% confidence interval for the true proportion of customers who cannot log in due to caps lock is (0.128, 0.185). Is it reasonable to believe the true proportion of customers who cannot log in due to caps lock is greater than 13%?

Yes, because most of the values in the interval are above 0.13.
Yes, because the center of the interval is 0.1565, which is greater than 0.13.
No, because 0.13 is in the interval.
No, because there are values in the interval that are less than 0.13.

Answers

Answer:

It’s D for heaven sake !

No, because there are values in the interval that are less than 0.13.

Step-by-step explanation:

Winnie has 7 soccer trophies she wants to arrange in an array. How many different arrays are possible?

Answers

Answer:

5040 possible arrangements

Step-by-step explanation:

Given

[tex]Trophies = 7[/tex]

Required

Possible arrangements

The 1st can be placed in any 7 positions

The 2nd, in 6 positions

-----

--

-

Up till the last in 1 position

So, the number of arrangements is:

[tex]Arrangements = 7 * 6 * 5 * 4 * 3 * 2 * 1[/tex]

[tex]Arrangements = 5040\ ways[/tex]

last year Kurt grew a pumpkin the had a mass of 12 3/8 kg. this year he grew a pumkin that was 2/3 as much What is the mass of the pumkin Kurt grew this year?​

Answers

Answer:

8 2/8 kg or 8 1/4 kg

Step-by-step explanation:

Multiply 2/3 by 12 3/8 to find 2/3 of Kurt's last year pumpkin

The fraction 2/3 of 12 3/8 is 8 1/4 thus the mass of the pumpkin Kurt grew this year is 8 1/4.

What is a fraction?

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

The value that appears above the horizontal line is referred to as the numerator.

Given that,

Mass of pumpkin last year = 12 3/8

It's grown by 2/3 factor this year.

2/3 of 12 3/8 → 2/3(12 + 3/8)

⇒ 8 + 2/8

⇒ 8 + 1/4 = 8 1/4

Hence "The fraction 2/3 of 12 3/8 is 8 1/4 thus the mass of the pumpkin Kurt grew this year is 8 1/4".

For more about fractions,

https://brainly.com/question/10354322

#SPJ2

Find the value of the length x rounded to 1 DP.

The diagram is not drawn accurately
PLEASE HELP ASAP WILL GIVE BRAINLIEST TO CORRECT ANSWER

Answers

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The value of x is 6.2 units.

What is Tangent (Tanθ)?

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The value of x is,

x = AB - AC

x = 31(Tan 37°) - 31(Tan 29°)

x = 6.17659 ≈ 6.2 units.

Hence, the value of x is 6.2 units.

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

#SPJ1

Solve the proportion (last was wrong, i apologize to those who answered my previous one!!)

11/s = s/-6

Answers

Answer:

x=±√(-66)

(there is no real solution)

Step-by-step explanation:

Answer:

hngbkx8uff

jrgjgk

Step-by-step explanation:

jgjk

TRAINGLE CONGRUENCE i think ... (PICTURE INCLUDED) PLA EXPLAIN HOW!!!

Answers

Answer:

Step-by-step explanation:

Cos ∅ = [tex]\frac{Adjacent side}{Hypotenuse}[/tex]

Cos 48° =[tex]\frac{38}{x}[/tex]

0.67 = [tex]\frac{38}{x}[/tex]

0.67*x = 38

x = [tex]\frac{38}{0.67}[/tex]

x = 56.71

x = 56.7

3) Write an explicit
formula for the
sequence:
45, 41, 37, 33

Answers

Answer and Step-by-step explanation:

f(n) = 45 - 4(n - 1)

This is the explicit formula for the sequence.

45 is the initial amount, which is why it is by itself.

The change in the sequence is take away 4, so this becomes a negative 4, which is then multiplied by (n - 1), where n is the term in the sequence.

#teamtrees #PAW (Plant And Water)

52% of the total number of students in a school are boys. If there are 260 boys,​

Answers

Question:

52% of the total number of students in a school are boys. If there are 260 boys,​ how many students are there in total? how many of them are girls?

Answer and Step-by-step explanation:

The total amount of students is 500.

Yo get this by dividing 260 by 52%, or 0.52

Now, we know 260 is the amount of boys, so to find the amount of girls, we subtract 260 from 500.

500 - 260 = 240.

There are 240 students that are girls.

This also means that 48% of the total number of students in a school are girls.

#teamtrees #PAW (Plant And Water)

What is the volume of this rectangular prism?
3/5cm 4/3cm 3cm

Answers

Answer:

The volume is 2.4

Answer:

2.4 cm

Step-by-step explanation:

Length× Width × Height

[tex]\frac{3}{5}[/tex] × [tex]\frac{4}{3}[/tex] × [tex]\frac{3}{1}[/tex] = [tex]\frac{36}{15}[/tex]

[tex]\frac{36}{15} = \frac{12}{5}[/tex]

12÷5= 2.4

The length of the carpet is 8 yards 9 inches.
How long is the carpet in inches? Enter your answer in the box.​

Answers

Multiply 8 by 9, this equals 72

Your answer is 72 Inches

Answer:

297 inches 100% sure it's correct.

Step-by-step explanation:

HELP PLEASE PLEASE!!!​

Answers

Answer:

a) 20 feet

Step-by-step explanation:

8ft shadow - 5ft

32ft shadow - [tex]\frac{32}{8}[/tex] × 5ft = 20ft

Answer:

A

Step-by-step explanation:

Ratio from shadow to object

8:5

Given Shadow of tree = 32ft, (8x4)

Height of Tree = 5x4 = 20ft

A

thank you for hurrying here is the very last one Explain how you would find the perimeter of this triangle.

Answers

Step-by-step explanation:

Use the method of TOA CAH SOH.

[tex]tan(51.3) = \frac{opp}{adj} \\ \tan(51.3) = \frac{u}{4} \\ u = 4 \tan(51.3) [/tex]

[tex] cos(51.3) = \frac{adj}{hypo} \\ \cos(51.3) = \frac{4}{v} \\ v \cos(51.3) = 4 \\ v = \frac{4}{ \cos(51.3) } [/tex]

Perimeter of triangle = Sum of all sides =

[tex]u \: + \: v + 4[/tex]

Answer:

use right angeled triangle method.

Went out to eat on his birthday 4 shot 3 dead in tha worst way

Answers

Answer:

That's unfortunate. Is everything okay?

50 points


Look at the work for the following function. What mistake did they make when using the quadratic formula to find the solutions? What are the real solutions to the function?

Answers

Answer:

see below

Step-by-step explanation:

whenever there is negative number being squared, you need to add the brackets so that you inside the - 1 in front of the number

so this step is wrong

[tex] \sqrt{ - 9 { }^{2} - 4(1)(20) } [/tex]

the -9 ² , you must include the brackets to include the -1 in front of the 9

so it should be

[tex] \sqrt{( - 9) {}^{2} - 4(1)(20) } [/tex]

so you will get = 1

and then you continue with other parts of the formula and you will get real solutions

hope this helps

please mark it brainliest

inside the radical should be 81-80 which would be 1 of course and that leaves real solutions. answers are 5 & 4

Why should Emily use a wire to connect point 2 to point 4? A) Metal wire is always expensive to work with. B) Metal is a good insulator of electricity. C) Metal wire is a good conductor of electricity. D) Metal is an inexpensive material to work with.

Answers

Answer:

c.)  Metal wire is a good conductor of electricity.

Step-by-step explanation:

https://byjus.com/questions/why-are-metals-good-conductors-of-electricity/#:~:text=Metals%20are%20an%20excellent%20conductor,of%20the%20interacting%20metal%20ions.

"Metals are an excellent conductor of electricity and heat because the atoms in the metals form a matrix through which outer electrons can move freely. Instead of orbiting their respective atoms, they form a sea of electrons that surround the positive nuclei of the interacting metal ions."

Hope this helped!

Stay safe! <3

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