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nata0808 [166]
3 years ago
8

A boat uses two pontoons to float. Each pontoon consists of a cylinder with a hemisphere at each end, as shown. Find the total v

olume of the two pontoons. Round your answer to the nearest whole number.

Mathematics
1 answer:
iragen [17]3 years ago
4 0

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)

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