Question

Water flows at a rate of 8000 cubic inches per minute into a cylindrical tank. The tank has a diameter of 128 inches and a height of 72 inches. What is the height, in inches, of the water in the tank after 10 minutes? Round your answer to the nearest tenth.

Answer 1

The height of the water = 6.2 in. to the nearest tenth

Explanation:

∵ The rate of flows of water into the tank = 8000 in.³/min.

∴ The volume of the water in the tank after 10 min. = 8000 × 10 = 80000 in.³

∵ The water take the shape of the tank

∴ The height of the water = volume of water ÷ Area of the base of the tank

∵ The tank is cylinder with diameter 128 in. and height 72 in.

∴ The area of the base of the tank = π(128/2)²

∴ The height of the water =
`(80000)/(\pi(64)^(2))=6.2169899`

∴ The height of the water = 6.2 in. to the nearest tenth