Question

The number of gallons g in a circular swimming pool varies jointly with the square of the radius r^2 and the depth d. If g = 754 when r = 4 and d = 2 , find the number of gallons in the pool when r = 3 and d = 1.5 .

Answer 1

318.09 gal

Explanation:

We know that the number of gallons (g) varies jointly with the square of the radius (r^2) and the depth (d), which means that the variation we can use to solve is:

g = k * r^2 * d

where k is the constant of proportionality. To find the value of k, we can use the given information:

When r = 4 and d = 2, g = 754:

754 = k * 4^2 * 2

754 = 32k

k = 23.5625

Now we can use this value of k to find the number of gallons in the pool when r = 3 and d = 1.5:

g = k * r^2 * d

g = 23.5625 * 3^2 * 1.5

g = 318.09375

Therefore, the number of gallons in the pool when r = 3 and d = 1.5 is approximately 318.09 gal