Question

A cone shaped hole is drilled into a solid cube of metal as shown.

Answer 1

Given

The diagram is given where cube is drilled with a hole in a shape of cone.

The cube length is 9 cm.

Step-by-step explanation

To find the volume of metal after the hole is drilled.

Find the volume of cube.

`\begin{gathered} V=a^3 \\ V=9^3=729cm^3 \end{gathered}`

Find the volume of cone, where radius is side of cube is divide by 2.

`r=(9)/(2)=4.5cm`

The volume of cone is

`\begin{gathered} V=(1)/(3)\pi r^2h \\ V=(1)/(3)*3.14*4.5^2*9 \\ V=3*3.14*4.5*4.5 \\ V=190.755cm^3 \end{gathered}`

To determine the volume of metal after the hole is drilled , subtract the volume of cube from the volume of cone.

`729-190.755=538.245cm^3`

Answer

The volume of metal after the hole is drilled