Question

Find the volume of the composite figure in the terms of pi

Answer 1

Step-by-step explanation:

Given;

We are given a half sphere placed inside a cylinder.

The dimensions of both solid shapes are as follows;

`\begin{gathered} Hemi-sphere: \\ radius=3ft \end{gathered}`
`\begin{gathered} Cylinder: \\ radius=3ft \\ height=5ft \end{gathered}`

The volume of a hemisphere is given by the formula;

`Volume=(2)/(3)\pi r^3`

We shall substitute the values given and we'll have;

`Volume=(2)/(3)*\pi*3^3`
`Volume=(2)/(3)*\pi*27`
`Volume=18\pi ft^3`

The volume of a cylinder is given by the formula;

`Volume=\pi r^2h`

We now have;

`Volume=\pi*3^2*5`
`Volume=45\pi ft^3`

Therefore, the volume of the composite figure is;

`Volume=hemisphere+cylinder`
`Volume=18\pi+45\pi`
`Volume=63\pi ft^3`

ANSWER:

`Volume\text{ }of\text{ }the\text{ }composite\text{ }figure=63\pi ft^3`