Question

A boat uses two pontoons to float. Each pontoon consists of a cylinder with a hemisphere at each end, as shown. Find the total volume of the two pontoons. Round your answer to the nearest whole number.

Answer 1

`20 \: ft^(3)`

Explanation:

Let's find the volume of 1 pontoon first.

Volume of pontoon

= volume of cylinder + 1 sphere

(since there are 2 hemispheres in total)

Volume of cylinder=
`\pi {r}^(2) h`

Volume of sphere=
`(4)/(3) \pi {r}^(3)`

Radius= 1÷2

Radius= 0.5 ft

Volume of cylinder

`= \pi(0.5)^(2) (12) \\ = 3\pi \: {ft}^(3)`

Volume of sphere

`= (4)/(3) \pi(0.5)^(3) \\ = (1)/(6) \pi \: {ft}^(3)`

Volume of 1 pontoon

`= 3\pi + (1)/(6) \pi \\ =(19)/(6) \pi`

Total volume of 2 pontoons

`= 2((19)/(6) \pi) \\ = (19)/(3)\pi \\ = 20 \: {ft}^(3)`

(nearest whole number)