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adell [148]
3 years ago
13

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:
zubka84 [21]3 years ago
3 0

Answer:

Total \approx 20ft^3

Step-by-step explanation:

Given

h = 12ft --- height of the cylinder

d =1ft --- the diameter of the hemispheres at both end and the cylinder

See attachment for pontoon

Required

Determine the volume

First, calculate the radius (r)

r = \frac{1}{2} * d

r = \frac{1}{2} * 1ft

r = 0.5ft

Next, the volume of the cylinder

V_1 = \pi r^2h

V_1 = 3.14 * 0.5^2 * 12

V_1 = 9.42ft^3

Two hemispheres make up a sphere. So, we simply calculate the volume of a sphere.

V_2 = \frac{4}{3}\pi r^3

V_2 = \frac{4}{3} * 3.14* 0.5^3

V_2 = 0.52ft^3

So, the volume of 1 pontoon is:

V_3 = V_1 + V_2

V_3 = 9.42ft^3 + 0.52ft^3

V_3 = 9.94ft^3

The volume of both is:

Total = 2 * V_3

Total = 2 * 9.94ft^3

Total = 19.88ft^3

Total \approx 20ft^3

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