Question

A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.)

Answer 1

Answer:

Volume of water = 1800π ≈ 5655m³

Step-by-step explanation:

If we assume that "y" varies from north to south since height varies from south to north. We will obtain;

h(y) = ay + b

Thus,

At, h(-20) = 2 ; 2 = -20a + b ___ eq(1)

At, h(20) = 7; 7 = 20a + b ___ eq(2)

Add eq 2 to eq 1;

7 + 2 = 20a - 20a + b + b

9 = 2b; b = 9/2

Plug in 9/2 for b in eq 2;

7 = 20a + 9/2

Multiply through by 2;

14 = 40a + 9

40a = 14 - 9; a = 5/40 = 1/8

Thus, h(y) = (1/8)a + (9/2)b

The rest of the process involves double integral, so i have attached it for clarity.