Question

A rectangular container that measures 2cm x 11cm x 20cm is completely filled with water. The water is then poured into a hollow cylindrical container of base radius 5cm.

What is the height of water in the cylindrical container?

Answer 1

height of water = 5.60 cm

Explanation:

To solve this problem, we must first calculate the volume of water present. Since the rectangular container is completely filled, the volume of water is the same as the volume of the container.

∴ Volume of water = volume of rectangular container

= length × width × height

= 2 cm × 11 cm × 20 cm

= 440 cm³

Therefore the volume of the water is 440 cm³.

The water is poured into a cylindrical container. Therefore, to calculate the height of the water in the cylindrical container, we can use the formula for the volume of a cylinder, and then solve for height:

Volume =
`\pi r^2 h` = 440

⇒
`\pi * (5)^2 * h = 440`

⇒
`25\pi * h = 440`

⇒
`h = (440)/(25\pi )`

⇒ h = 5.60 cm

The height of water in the cylindrical container is 5.60 cm.