Question

Find the volume of the sphere with d=163. Round your answer to the nearest tenth. Use 3.14 to represent pie.

Answer 1

To find the volume, V, of a sphere, the formula is

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \text{Where r is the radius} \end{gathered}$

Given that the diameter, d, of the sphere is 163 units, the radius, r, is

$r=\frac{d}{2}$

Where d = 163, r will be

$r=\frac{d}{2}=\frac{163}{2}\text{ units}$

Substitute for r into the formula for the volume, V, of a sphere

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \text{Where r}=\frac{163}{2}\text{ and }\pi\text{ is taken as 3.14} \\ V=\frac{4}{3}\times3.14\times(\frac{163}{2})^3 \\ V=\frac{4}{3}\times3.14\times\frac{4330747}{8} \\ V=\frac{3.14\times4330747}{3\times2}=2266424.263333333 \\ V=2266424.3units^3\text{ (nearest tenth)} \end{gathered}$

Hence, the volume, V of the sphere is 2266424.3 unit³ (nearest tenth)