Quiz about Pyramid Volume Homework help and answers

Question 1

What is the formula to find the volume of a pyramid?

Accepted Answer

$$V=\frac{1}{3}B\cdot h$$

Answer

$$V=bh$$

Answer

$$V=Bh$$

Answer

$$V=\frac{1}{2}\left(b_1+b_2\right)\cdot h$$

Question 2

Which formula do you use to find the volume of this figure?

Accepted Answer

$$V=\frac{1}{3}\pi r^2\cdot h$$

Answer

$$V=\pi r^2$$

Answer

$$V=\pi r^2\cdot h$$

Answer

$$V=b\cdot h$$

Question 3

Which shape is at the base of this pyramid?

Accepted Answer

A triangle, so $$B=\frac{1}{2}b\cdot h$$

Answer

A rectangle, so $$B=b\cdot h$$

Question 4

What is the 3D height of the pyramid?

Accepted Answer

8 ft

Answer

12 ft

Question 5

Which formula should you use?

Accepted Answer

$$V=\frac{1}{3}\pi\left(9.5\right)^2\cdot12$$

Answer

$$V=\frac{1}{3}\pi\left(19\right)^2\cdot12$$

Answer

$$V=\left(19\right)^2\cdot12$$

Answer

$$V=\pi\left(9.5\right)^2\ \cdot12$$

Question 6

What is the volume of this figure?

Accepted Answer

$$V=1134.11\ m^3$$

Answer

$$V=4536.46\ m^3$$

Answer

$$V=13609.37\ m^3$$

Answer

$$V=3402.34\ m^3$$

Question 7

This already gives you the base! So which formula correctly uses $$V=\frac{1}{3}B\cdot h$$ ?

Accepted Answer

$$V=\frac{1}{3}\cdot110\cdot11$$

Answer

$$V=110\ \cdot\left(8\cdot5\right)\cdot11$$

Answer

$$V=\frac{1}{3}\cdot8\cdot11$$

Question 8

What is the volume of this figure?

Accepted Answer

$$V=403.33\ mm^3$$

Answer

$$V=48400\ mm^3$$

Answer

$$V=9680\ mm^3$$

Question 9

Uh oh....Pythagorean theorem...you are missing the base of this SQUARE pyramid and need to use the pythagrean theorem to find it. Which formula should you use?

Accepted Answer

$$b^2+7.2^2=9.7^2$$

Answer

$$7.2^2+9.7^2=b^2$$

Question 10

Uh oh....Pythagorean theorem...you just found out the base of the triangle is 6.5 in, so what is the area of the square base?

Accepted Answer

B = 13*13 = 169

Answer

B = 6.5*6.5 = 42.25

Question 11

The 2D base of this pyramid is a triangle!

What is the height of the triangle?

Accepted Answer

We don't know...you have to use Pythagorean theorem again...

Answer

24 ft

Answer

16 ft

Question 12

The 2D base of this pyramid is a triangle!

What is the height of the triangle?

Accepted Answer

13.86

Answer

$$8^2+h^2=\ 16^2$$

Not the answer, just help

Answer

It's not 0 because we have to cut the base in half to make a right triangle for Pythagorean theorem

Answer

17.89

Question 13

Which formula is correct for this pyramid?

Accepted Answer

$$V=\ \frac{1}{3}\cdot\left(\frac{1}{2}\cdot13.86\cdot16\right)\cdot24$$

since the base is a triangle

Answer

$$V=\ \frac{1}{3}\cdot\left(13.86\cdot16\right)\cdot24$$

since the base is a triangle

Question 14

Uh oh....Pythagorean theorem...you have the slant height of this cone (yuck!) and you need to find the height of the cone instead...which should you use?

Accepted Answer

$$h^2+5.2^2=17.3^2$$

Answer

$$10.4^2+17.3^2=h^2$$

Answer

$$h^2+10.4^2=17.3^2$$

Answer

$$5.2^2+17.3^2\ =\ h^2$$

Question 15

What is the volume of the cone?

Accepted Answer

467.22

Answer

1868.88

Answer

5606.64

Answer

1401.66

Question 16

This is simply one BIG GREY cone with the top little CONE cut out (aka subtracted). You need to find the volume of the BIG GREY and then subtract the little CONE. What is the volume of the BIG GREY?

Accepted Answer

$$V=\frac{1}{3}\pi\left(9\right)^2\cdot25$$

Answer

$$V=\frac{1}{3}\pi\left(18\right)^2\cdot25$$

Answer

$$V=\frac{1}{3}\pi\left(9\right)^2\cdot15$$

Answer

$$V=\frac{1}{3}\pi\left(4\right)^2\cdot10$$

Question 17

A cone with a radius of 6 meters has a volume of 542.87 m3.

Find the slant height of the cone.

Accepted Answer

slant = 15.6 m

Answer

This means, find the height of the cone, then set up Pythagorean theorem

$$slant\ ^2=\ 6^2+h^2$$

Answer

You can find the height of the cone with algebra since $$V=\frac{1}{3}\pi\cdot\left(6\right)^2\cdot h$$

Answer

That means $$542.87\ =\ 37.699\ \cdot h\ $$ if you simplify everything.

From there just divide both sides by 37.699

Answer

h = 14.4 but again, you're looking for SLANT HEIGHT. So use $$14.4^2+6^2=slant^2$$

Pyramid Volume Homework help and answers

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