Question

Find the total volume of the following composite figure with

h=7.5

and

r=3.6

Use 3.14 for LaTeX: \piπ.

Round to the nearest hundredth.

Answer 1

Given:

The height of the given fig = 7.5 unit

The radius of the given fig = 3.6 unit

To find the volume of the given composite figure.

Formula

The volume of the given fig

`V = V_(1)+V_(2)`

where,

`V_(1)` be the volume of the cone

`V_(2)` be the volume of the semicircle

`V_(1)=\pi r^(2) h`, r be the radius and h be the height

`V_(2) = (2)/(3) \pi r^(3)`, r be the radius

Now,

Putting, r= 3.6, h = 7.5 and π = 3.14 we get,

`V_(1) =(3.14)(3.6^(2) )(7.5)` cube in

or,
`V_(1)= 305.208` cube in

And,

`V_(2) =(2)/(3) (3.14)(3.6^(3))` cube in

or,
`V_(2) = 97.67` cube in

So,

`V = 305.208+97.67` cube in

or,
`V = 402.878` = 402.88 cube in

Hence,

The volume of the given figure is 402.88 cube in.