Question

A paperweight, the shape of a hemisphere, fits snugly inside a cylinder-shaped box with a radius of 9 cm. A cone fits snugly inside the paperweight hemisphere.

What is the volume of the cylinder in terms of pi

? Show all work.

What is the volume of the cone in terms of pi

? Show all work.

Estimate the volume of the hemisphere in terms of pi

by calculating the average of the volumes of the cylinder and cone. Show all work.

Find the hemisphere’s diameter if its radius is 12 cm.
cm

Find the hemisphere’s diameter if its radius is
m.
m

Find the hemisphere’s diameter if its radius is 12.004 ft.
ft

Find the hemisphere’s radius if its diameter is 12 cm.
cm

Find the hemisphere’s radius if its diameter is
m.
m

Find the hemisphere’s radius if its diameter is 12.004 ft.
ft

Answer 1

The volume of the cylinder is given by the formula: V = πr^2h, where r is the radius and h is the height. In this case, the height is equal to the diameter of the hemisphere (which is also the diameter of the paperweight), so we have:

V = π * 9^2 * (2 * 9) = 904π cm^3

The volume of the cone is given by the formula: V = (1/3)πr^2h, where r is the radius and h is the height. In this case, the height is equal to the diameter of the hemisphere, and the radius is half the diameter, so we have:

V = (1/3)π * (9/2)^2 * (2 * 9) = 188π cm^3

To estimate the volume of the hemisphere, we find the average of the volumes of the cylinder and cone:

V = (904π + 188π) / 2 = 546π cm^3

If the radius of the hemisphere is 12 cm, its diameter is 2 * 12 = 24 cm.

If the radius of the hemisphere is x m, its diameter is 2 * x m.

If the radius of the hemisphere is 12.004 ft, its diameter is 2 * 12.004 = 24.008 ft.

If the diameter of the hemisphere is 12 cm, its radius is 12 / 2 = 6 cm.

If the diameter of the hemisphere is x m, its radius is x / 2 m.

If the diameter of the hemisphere is 12.004 ft, its radius is 12.004 / 2 = 6.002 ft.