Question

Inez carved a wooden cone from a

cylindrical piece of wood. The cylindrical
piece of wood had a radius of 3 inches
and a height of 15 inches. The cone had
the same radius as the cylinder but was
2 inches shorter. About what volume of
wood did Inez remove from the cylinder to
make the cone?

Answer 1

123 inches³

Explanation:

Hi there!

Objective: Find the volume of the cone

We know that the cylinder had a radius of 3 inches and it had a height of 15 inches.

Because the cone had the same radius of the cylinder, we know that it has a radius of 3 inches. And because it was 2 inches shorter, it has a height of 13 inches (15-2=13).

`V=(1)/(3) \pi r^2h` where r is the radius of the cone and h is its height

Plug in the known information (r=3 and h=13)

`V=(1)/(3) \pi (3)^2(13)\\V=(1)/(3) \pi (9)(13)\\V=(1)/(3) \pi(117)\\V=39\pi\\V=123`

Therefore, the Inez removed about 123 inches³ of wood from the cylinder to make the cone.

I hope this helps!