Question

4. The altitude of a right circular cone is 15 and the radius of its base is 8. A cylindrical hole of diameter 4 is drilled through the cone, with its axis along the axis of the cone, leaving a solid. What is the volume of this solid?

Answer 1

Given:

The altitude of a right circular cone = 15

The radius of the base = 8

A cylindrical hole of diameter 4 is drilled through the cone, with its axis along the axis of the cone.

So, the radius of the cylinder = 2

We will find the height of the cylinder using the ratio and proportional

Let the height of the cylinder = h

so,

`\begin{gathered} (h)/(15)=(6)/(8) \\ \\ h=(6\cdot15)/(8)=11.25 \end{gathered}`

So, the height of the cylinder = 11.25

The volume of the solid = the volume of the cone - the volume of the cylinder

The volume of the cone =

`(1)/(3)\pi\cdot r^2h=(1)/(3)\cdot3.14\cdot8^2\cdot15=1004.8`

The volume of the cylinder =

`\pi\cdot r^2\cdot h=3.14\cdot2^2\cdot11.25=141.3`

So, the volume of the solid =

`1004.8-141.3=863.5`

so, the answer will be: Volume of the solid = 863.5