Question

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

to the radius of the hemisphere removed, what volume remains of the hemisphere?
(1) 483 cubic centimeters
(2) 536 cubic centimeters
(3) 589 cubic centimeter
(4) 614 cubic centimeters​

Answer 1

The volume remaining is approximately 536 cm³

Explanation:

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

`\text{volume hemisphere} = (4)/(6)*pi*r^3\\\text{volume hemisphere} = (4)/(6)*pi*8^3 = 1072.33 \text{ } cm^3`

While the volume of the cone is:

`\text{volume cone} = (\pi*r^2*h)/(3)\\\text{volume cone} = (\pi*(8)^2*8)/(3)\\\text{volume cone} = (\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