Question

A hemisphere has a radius of 8 centimeters. If a cone whose diameter is the same and whose height is equal

Answer 1

Answer:

The volume remaining is approximately  536 cm³

Step-by-step explanation:

The volume of a hemisphere is the volume of the sphere divided by two, therefore it's formula is:

$\text{volume hemisphere} = \frac{4}{6}*pi*r^3\\\text{volume hemisphere} = \frac{4}{6}*pi*8^3 = 1072.33 \text{ } cm^3$

While the volume of the cone is:

$\text{volume cone} = \frac{\pi*r^2*h}{3}\\\text{volume cone} = \frac{\pi*(8)^2*8}{3}\\\text{volume cone} = \frac{\pi*512}{3} = 536.1651 \text{ } cm^3$

What remains on the hemisphere is the difference between these volumes, therefore:

$\text{remaining volume} = 1072.33 - 536.17 = 536.16 \text{ } cm^3$

The volume remaining is approximately  536 cm³