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

Answer:

The diameter of the hemisphere is 20.4 centimeters.

Step-by-step explanation:

The volume of an hemisphere is given by:

$V = \frac{2 \pi r^{3}}{3}$

In this problem, we have that:

$V = 2233$

So

$\frac{2 \pi r^{3}}{3} = 2233$

$2\pi r^{3} = 3*2233$

$r^{3} = \frac{3*2233}{2\pi}$

$r = \sqrt[3]{\frac{3*2233}{2\pi}}$

$r = 10.2$

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.