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

Answer:

$20 \: ft^{3}$

Step-by-step 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=$\frac{4}{3} \pi {r}^{3}$

Radius= 1÷2

Radius= 0.5 ft

Volume of cylinder

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

Volume of sphere

$= \frac{4}{3} \pi(0.5)^{3} \\ = \frac{1}{6} \pi \: {ft}^{3}$

Volume of 1 pontoon

$= 3\pi + \frac{1}{6} \pi \\ =\frac{19}{6} \pi$

Total volume of 2 pontoons

$= 2(\frac{19}{6} \pi) \\ = \frac{19}{3}\pi \\ = 20 \: {ft}^{3}$

(nearest whole number)