Question

What is the diameter of a hemisphere with a volume of 2233\text{ cm}^3,2233 cm 3 , to the nearest tenth of a centimeter?

Answer 1

The diameter of the hemisphere is 20.4 centimeters.

Explanation:

The volume of an hemisphere is given by:

`V = (2 \pi r^(3))/(3)`

In this problem, we have that:

`V = 2233`

So

`(2 \pi r^(3))/(3) = 2233`

`2\pi r^(3) = 3*2233`

`r^(3) = (3*2233)/(2\pi)`

`r = \sqrt[3]{(3*2233)/(2\pi)}`

`r = 10.2`

The radius is 10.2 centimeters.

The diameter is double the radius. So:

2*10.2 = 20.4

The diameter of the hemisphere is 20.4 centimeters.