Sphere Formula

Some of the important formulas related to spheres are listed below.

Diameter, d = 2r

Surface area, $$SA=4\pi r^2$$

Volume, $$V=\frac{4\pi }{3}{r}^3$$

Let’s look at an example to see how to use these formulas!

Question: Find the surface area of a sphere whose volume is 38808 cm3.

Solution:

$$V=\frac{4\pi }{3}{r}^3=38808\Rightarrow \frac{4}{3}\times \frac{22}{7}\times r^3=38808\Rightarrow r^3=\frac{38808\times 21}{88}=9261\Rightarrow r=21cm$$

$$SA=4\pi r^2=4\times \frac{22}{7}\times {21}^2=4\times 22\times 3\times 21=5544c{m}^2$$

Why don’t you try to solving a problem for practice?

Question: The surface area of a sphere is 616 cm2. Find its volume.

Options:

(a) $$143.34c{m}^3$$

(b) $$616.67c{m}^3$$

(c) $$437.34c{m}^3$$

(d) $$1437.34c{m}^3$$ 

Answer: (d)

Solution:

$$SA=616c{m}^2$$

$$SA=4\pi r^2\Rightarrow 4\pi r^2=616\Rightarrow r^2=\frac{616\times 7}{4\times 22}=49\Rightarrow r=7cm$$

$$V=\frac{4\pi }{3}{r}^3=\frac{4}{3}\times \frac{22}{7}\times 7^3=1437.34c{m}^3$$