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

`Total \approx 20ft^3`

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 = (1)/(2) * d`

`r = (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 = (4)/(3)\pi r^3`

`V_2 = (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`