Question

What is the volume of the composite figure if both the height and the diameter of the cylinder are 2.5 feet? Give the exact answer and approximate to two decimal places.

Answer 1

`\begin{gathered} V=(125)/(24)\pi ft^3 \\ V\cong16.36ft^3 \end{gathered}`

Explanation:

Given:

Diameter = 2.5 ft

The radius is half the diameter, so

Radius = 1.25 ft

Height = 2.5 ft

To calculate the volume of the figure, we must calculate the volume of the hemisphere and the volume of the hemisphere separately and then add them.

Therefore:

Cylinder volume

`\begin{gathered} V_c=\pi\cdot r^2\cdot h \\ \text{ we replacing} \\ V_c=(125)/(32)\pi\cong12.27ft^3 \end{gathered}`

hemisphere volume

`\begin{gathered} V_h=(2)/(3)\pi\cdot r^3 \\ V_h=(2)/(3)\pi(125)/(64)=(125)/(96)\pi=4.09ft^3 \end{gathered}`

We add to obtain the volume of the figure:

`\begin{gathered} V=(125)/(32)\pi+(125)/(96)\pi=(125)/(24)\pi ft^3 \\ V=12.27+4.09=16.36ft^3 \end{gathered}`

The exact volume is 125/24 cubic feet and the approximate volume is 16.36 cubic feet.