SURFACE AREA AND VOLUME OF A SPHERE

CONTENT

1. Surface Area of a Sphere
2. Volume of a Sphere

Surface Area and Volume of a Sphere

Sphere

The diagram below shows a solid sphere of radius

Formulae

1. Curved surface area of sphere = \(4πr^2\)

2. Volume of sphere = \(\frac{4}{3}πr^3\)

3. Volume of a hemisphere = \(\frac{2}{3}πr^3\)

4. Total surface area of a hemisphere = \(3 πr^2\)

Examples:

1. Find the volume and curved surface area of a sphere of radius 9cm correct to 4 s.f. (Take \(π=3.142\))

Solution:

Volume of sphere \(= \frac{4}{3} πr^3\)

\(π=3.142\), \(r = 9cm =3cm^3 \).

\(Volume = \frac{4}{3} × \frac{3.142}{1} × 9^3cm^3 \\ = 3054.024cm^3\\ = 3054cm^3 \text{ (4 s.f.)}\)

Curved surface area \(=4 πr^2 \), \(π=3.142\)  \(r=9cm\)

Curved surface area \(=4×3.142×9^2 cm^2 \\ =1018.008 cm^2 \\=1018cm^2 \text{ (4 s.f.)}\)

2. The volume of a sphere is \(2100cm^3\), and its radius is \(x cm\).