# How to find Surface Area and Volume of Composite Figures

Now, let’s look at composite figures in 3D. In order to calculate the volume of such composite figures, you have to separate the composite figure into smaller figures so that you can determine the volume of each, then add them up.

Example 1

Find the volume of the composite figure.

You can separate the figure into a cylinder and a cone, and find the volume of each of them.

Volume of the cylinder:

 $V=\pi {r}^{2}h=\pi \cdot {6}^{2}\cdot 9\approx 1017.88\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$

Volume of the cone:

 $V=\frac{\pi {r}^{2}h}{3}=\frac{\pi \cdot {6}^{2}\cdot 5}{3}\approx 188.50\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$

Volume of the whole figure:

 $V\approx 1017.88+188.50\approx 1206.38\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$

Example 2

Find the volume of this ice cream

Half of the scoop of ice cream is inside the wafer. The volume of the wafer is the volume of a cone:

 ${V}_{\text{cone}}=\frac{\pi \cdot {4}^{2}\cdot 15}{3}\approx 251.2\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$

The volume of the entire scoop of ice cream is the volume of a sphere:

 ${V}_{\text{sphere}}=\frac{4\cdot \pi \cdot {4}^{3}}{3}\approx 267.95\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$

If you now add the volume of the scoop of ice cream to the volume of the cone, you will be adding the entire ice cream scoop. But half of the scoop is inside the wafer cone, so you can’t count that volume twice! You have to divide the volume of the sphere by 2 first. Then you can add it to the volume of the cone to find the total volume of the ice cream.

The volume of the entire ice cream is

 $V\approx 251.2\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}+\frac{267.95\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}}{2}\approx 385.18\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{3}$