Surface Area and Volume Of Spheres - SS3 Mathematics Lesson Note

A sphere is the locus of points in space equidistant from one point called the center of the sphere.

A sphere can be split into two equal halves called a hemisphere.

\[Surface\ area\ of\ a\ sphere = 4\pi r^{2}\]

\[Volume\ of\ a\ sphere = \ \frac{4}{3}\pi r^{3}\]

Example 1 A sphere has a diameter of \(42\ cm\). Calculate its surface area and volume. \((\pi = \frac{22}{7})\)

Solution

\(diameter = 42\ cm\), \(radius = \ \frac{42}{2} = 21\ cm\)

\[Surface\ area\ of\ a\ sphere = 4\pi r^{2} = 4 \times \frac{22}{7} \times \frac{21 \times 21}{1} = 5,544cm^{2}\]

\[Volume\ of\ a\ sphere = \ \frac{4}{3}\pi r^{3} = \frac{4}{3} \times \frac{22}{7} \times \frac{21 \times 21 \times 21}{1} = 38,808\ {cm}^{3}\]