Question

4. A glass decoration is made from a cylinder and cone that have the same height and share a base. The cone fits exactly inside the cylinder. Blue sand fully fills the cone, and green sand fully fills the space between the cone and the cylinder. The radius of base is 5 cms, and the height is 24cms. In terms of pi, what is the volume of green sand between the cone and the Cylinder.

Answer 1

Volume of Green Sand =
`400 \pi` cubic centimeters

Explanation:

The image is shown below.

We need to find volume of cone and volume of cylinder.

The green sand space is:

Volume of Cylinder - Volume of Cone

Formulas:

Volume of Cylinder =
`\pi r^2 h`

Volume of Cone =
`(1)/(3)\pi r^2 h`

Given, r = 5 and h = 24 (in centimeters), we find the green sand volume:

Volume of Green Sand = Volume of Cylinder - Volume of Cone =
`\pi r^2 h - (1)/(3) \pi r^2 h = (2)/(3) \pi r^2 h = (2)/(3) \pi (5)^2 (24) = (2)/(3) \pi (25)(24) = 400 \pi`

Volume of Green Sand =
`400 \pi` cubic centimeters