Question

A cylinder has a radius of 3 feet and a height of 7 feet. Which of the following can be used to calculate the volume of a cone that fits exactly inside the cylinder?

Answer 1

The formula
`(1)/(3)*3.14*3*3*7` is used to find the cone volume.

Explanation:

We know that the radius of cylinder is = 3 feet

Height of the cylinder is = 7 feet

Its volume can be found as :

`v=\pi r^(2)h`

=
`3.14*3*3*7=197.82` cubic feet

Now, volume of cone is given as :

`v=(1)/(3) \pi r^(2)  h`

This means, the volume of cone is one-third the volume of cylinder.

So, the volume of cone that can fit in the cylinder will be one-third the volume of cylinder.

`(1)/(3)*3.14*3*3*7 = 65.94` cubic feet

If we want to check we can say that the volume of cylinder is three times cone.
`65.94*3=197.82`

Therefore, a cone with volume 65.94 cubic feet will fit into a cylinder with volume 192.82.

Answer 2

means it has same base and same height

vcone=height times base times 1/3
base=circle=pir²


so
given
r=3
h=7

V=(1/3)(7)(pi3²)
V=(7/3)(9pi)
V=21pi

answer is 21pi cubic feet or aprox65.97 cubic feet