Question

A sphere has a radius of 2 inches. What is the approximate volume of half of the sphere?

Answer 1

• radius=r=2in

Volume:-

`\\ \rm\Rrightarrow V=(4)/(3)\pi r^3`

`\\ \rm\Rrightarrow V=(4)/(3)\pi (2)^3`

`\\ \rm\Rrightarrow V=(32\pi)/(3)in^3`

Half volume:-

`\\ \rm\Rrightarrow V=(16\pi)/(3)in^3`

Answer 2

16.8 in³ (nearest tenth)

Explanation:

Volume of a sphere

`V=\frac43 \pi r^3`

(where V is volume and r is the radius)

Volume of a hemisphere

`\textsf{Volume of a hemisphere}=\frac12 \ \textsf{Volume of a Sphere}`

`\implies V=\frac12 \cdot \frac43 \pi r^3=\frac23 \pi r^3`

Given:

• r = 2 in

`\begin{aligned}\implies V & =\frac23 \pi (2)^3\\\\ & =(16)/(3) \pi\\\\ & =16.8 \ \sf in^3 \ (nearest \ tenth)\end{aligned}`