Question

A cone with a radius of 3 feet and a height of 5 feet is placed on top of a cylinder as shown. Find the volume of the total figure interms of TT.

Answer 1

Step 1

State the formula for the volume of a cone.

`V=(1)/(3)\pi r^2h`

Where;

`\begin{gathered} r=3\text{ f}t \\ h=5ft \end{gathered}`

Step 2

Find the volume of the cone in the figure.

`\begin{gathered} V=(1)/(3)*\pi*3^2*5 \\ V=(\pi*9*5)/(3) \\ V=15\pi ft^3 \end{gathered}`

Step 3

State the formula for the volume of a cylinder

`V=\pi r^2h`

where;

`\begin{gathered} r=3ft \\ h=6ft \end{gathered}`

Step 4

Find the volume of the cylinder.

`\begin{gathered} V=\pi*3^2*6 \\ V=\pi*9*6 \\ V=54\pi ft^3 \end{gathered}`

The total volume of the figure is, therefore;

`\begin{gathered} V=\text{volume of cone + volume of cylinder} \\ V=15\pi+54\pi \\ V=69\pi ft^3 \end{gathered}`

The total volume of the figure in terms of π=69π cubic feet

Answer;69π cubic feet