Surface Area and Volume of Composite Solids

Topic Content:

A composite shape contains two or more basic shapes. To get the volume of the component shape, add the volume of the individual shapes that make up the composite. Similarly, to get the total surface area, add up the surface areas of the basic shapes.

Example 5.4.1:

In the diagram above, a cylinder is surmounted by a hemisphereA hemisphere is half the Earth's surface. The four hemispheres are the Northern and Southern hemispheres, divided by the equator (0° latitude), and the Eastern and Western hemispheres, divided by the... More bowl. Calculate the volume of the solid.

Solution

Volume of the solid = Volume of cylinder + Voume of hemisphere

Volume of cylinder = πr² h
= π x 3² x 20
= π x 9 x 20
= 180 π cm³

Voume of hemisphere = \( \frac{2}{3} \scriptsize \pi r^3 \\ = \frac{2}{3} \scriptsize \: \times \: \pi \: \times \: 3^3 \\ = \frac{2}{3} \scriptsize \: \times \: \pi \: \times \: 27 \\ = \scriptsize 2 \: \times \: \pi \: \times \: 6 \\ = \scriptsize 18 \: \pi \: cm^3 \)

Volume of the solid = 180 π cm³ + 18 π cm³

Volume of the solid = 198 π cm³

Example 5.4.2:

A water reservoir in the form of a cone mounted on a hemisphere is built such that the plane face of the hemisphere fits exactly to the base of the cone and the height of the cone is 6 times the radius of its base.

(a) Illustrate this information in a diagram.

(b) If the