Question

A company designs its packaging so that it is a cylinder with a diameter of 4 inches and a height of 7 inches with a cone on top that has a diameter of 4 inches and a height of 3 inches. Find the volume of this figure. Leave in terms of π.

A) 32π in3
B) 44π in3
C) 110π in3
D) 128π in3

Answer 1

the answer is 32pi because formulas: pi*r^2*H cylinder
1/3 pi*r^2*h

if you use your formula`s right
2^2 * 7= 28pi
then, (1/3)* 2^2 * 3=4pi
afetrwards you do 28pi+4pi=32pi

Answer 2

`The\ total\ volume\ is\ 32\pi\ inches^(3).`

Explanation:

Formula

`Volume\ of\ a\ cylinder = \pi r^(2) h`

Where r is the radius and h is the height.

As given

A company designs its packaging so that it is a cylinder with a diameter of 4 inches and a height of 7 inches.

`Radius (r) = (Diameter)/(2)`

`Radius (r) = (4)/(2)`

Radius (r) = 2 inches

Put in the formula

`Volume\ of\ a\ cylinder = \pi* 2* 2* 7`

`Volume\ of\ a\ cylinder =28 \pi`

Formula

`Volume\ of\ a\ cone = \pi r^(2) (h)/(3)`

Where r is the radius and h is the height.

As given.

cone on top of the cylinder that has a diameter of 4 inches and a height of 3 inches.

`Radius (r) = (Diameter)/(2)`

`Radius (r) = (4)/(2)`

Radius (r) = 2 inches

Put in the formula

`Volume\ of\ a\ cone = \pi* 2* 2* (3)/(3)`

`Volume\ of\ a\ cone = 4\pi`

Total area = volume of a cylinder + volume of a cone

`Total\ volume= 28\pi+ 4\pi`

`Total\ volume= 32pi\ inches^(3)`

`Therefore\ the\ total\ volume\ is\ 32\pi\ inches^(3).`