Question

Water flows at a rate of 6000 cubic inches per minute into a cylindrical tank. The tank has a diameter of 180 inches and a height of 72 inches. What is the height, in inches, of the water in the tank after 5 minutes? Round your answer to the nearest tenth.

Answer 1

The height of water in tank after 5 minutes is 1.2 inches

Solution:

Water flows at a rate of 6000 cubic inches per minute into a cylindrical tank

Therefore,

1 minute = 6000 cubic inches

Therefore, for 5 minutes, rate is given as:

5 minute = 5 x 6000 = 30000 cubic inches

The tank has a diameter of 180 inches and a height of 72 inches

Diameter = 180 inches

`Radius = (diameter)/(2) = (180)/(2) = 90`

Thus, radius = 90 inches

We know that, volume of the water filled in the cylindrical tank in 5 minutes is 30000 cubic inches

Volume of cylinder is given as:

`v = \pi r^2 h`

Where, "r" is the radius and "h" is the height of tank

`30000 = 3.14 * (90)^2 * h\\\\30000 = 25434 * h\\\\h = (30000)/(25434)\\\\h = 1.179 \approx 1.2`

Thus height of water in tank after 5 minutes is 1.2 inches