Question

A swimming pool is circular with a 30-ft diameter. The depth is constant along east-west lines and increases linearly from 5 ft at the south end to 10 ft at the north end. Find the volume of water in the pool. (Round the answer to the nearest whole number.)

Answer 1

Answer : The volume of water in the pool is, 2473 ft³

Explanation :

First we have to calculate the average depth.

Given:

Diameter = 30 ft

Depth range : 1 to 6 ft linearly

average depth =

Now we have to calculate the volume of water in the pool.

Volume = area × average depth

V = π × (radius)² × 3.5

V = π × (30/2)² × 3.5

V = π × (15)² × 3.5

V = π × 225 × 3.5

V = 3.14 × 225 × 3.5

V = 2472.75 ft³ ≈ 2473 ft³

Therefore, the volume of water in the pool is, 2473 ft³

Answer 2

5299 ft³

Step-by-step explanation:

diameter of pool, D = 30 ft

radius of pool, r = 15 ft

depth = 5 ft to 10 ft linearly

Average depth, h =
`(5+10)/(2)` = 7.5 ft

The volume of the cylinder is given by

`V = \pi r^(2)* h`

V = 3.14 x 15 x 15 x 7.5

V = 5298.75 ft³

V = 5299 ft³