Question

A swimming pool is circular with a 30-ft diameter. The depth is constant along east-west lines and increases linearly from 4 ft at the south end to 9 ft at the north end. Find the volume of water in the pool.

Answer 1

Answer: 1462.5π

Step-by-step explanation:

y is assumed to varies from south to north. Therefore, h(y) = ay + b

h(-15) = 4 = -15a + b   ................................(Eq 1)

h(15) = 9 = 15a + b     ................................(Eq 2)

(Eq 1) + (Eq 2)

(-15a + b) + (15a + b) = 13

2b = 13

$b = \frac{13}{2}$

Substitute b=6.5 into (Eq 1)

4 = (-15a) + (13/2)

15a = 6.5 - 4

$a = \frac{1}{6}$

Therefore, $h (y) = \frac{1}{6}y +\frac{13}{2}$

Next, integrate the equation to obtain the volume of water in the pool.

Attached are the calculation for the volume of water in the pool.

Answer 2

Answer:

Volume of water in pool = 1462.5π

Step-by-step explanation:

I have attached the explanation