Anders is using casts to make plaster figures. He has a cylinder cast that has a diameter of 8 inches and

is 24 inches tall. Anders uses a cone-shaped container with a diameter of 12 inches and a height of

16 inches to fill his casts. How many cone-shaped containers full of plaster will he need to completely fill

the cylinder cast?

Enter your answer in the box.

The given cylindrical container is used to fill the rectangular prism fish tank with water.

Two cone-shaped containers will be needed

Step-by-step explanation:

The key to finding the answer to this is to calculate the volumes of each of the shapes.

For the cylinder cast, the volume will be π * r^2 * h, where r is D/2 = 8/2 = 4 inches and h = 24 inches

V = π * 4^2 * 24 = 384 π inches^3

For the cone-shaped container, its volume is 1/3 * π * r^2 * h

where r is D/2 = 12/2 = 6 inches and h is 16 inches

The volume = 1/3 * π * 6^2 * 16 = 192 π inches^3

Thus, the number of cone-shaped containers needed to fill the casting will be the volume of the casting divided by the volume of the container

= 384 π / 192 π = 2