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:

$Total \approx 20ft^3$

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:

$Total = 2 * V_3$

$Total = 2 * 9.94ft^3$

$Total = 19.88ft^3$

$Total \approx 20ft^3$