A spherical water tank holds 10,500 ft^3 of water. What is the diameter of the tank?
To find the diameter of the tank, we first need to determine the radius of the tank.
The volume of a sphere is given by the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.
Given that the tank holds 10,500 ft^3 of water, we have:
10,500 = (4/3) * π * r^3
r^3 = (3/4π) * 10,500
r = ((3/4π) * 10,500)^(1/3)
Now, we can find the diameter by multiplying the radius by 2:
diameter = 2 * radius
Calculating the diameter using the formula, we get:
r = ((3/4π) * 10,500)^(1/3) = 17.27 ft
diameter = 2 * 17.27 ft = 34.54 ft
Therefore, the diameter of the tank is approximately 34.54 ft.