Question
A spherical water tank holds 7,500 ft cubed of water. What is the diameter of the tank?
Answers
GPT 3.5
To find the diameter of the tank, we first need to calculate the radius of the spherical tank using the formula for the volume of a sphere:
V = (4/3) * π * r^3
Given that the volume of the water in the tank is 7,500 ft^3, we can plug this value into the formula and solve for the radius:
7,500 = (4/3) * π * r^3
r^3 = (3/4) * (7,500 / π)
r = (3/4 * 7,500 / π)^(1/3)
r ≈ 9.67 ft
Once we have the radius of the tank, we can find the diameter by multiplying the radius by 2:
Diameter = 2 * radius
Diameter = 2 * 9.67 ft
Diameter ≈ 19.34 ft
Therefore, the diameter of the tank is approximately 19.34 feet.
V = (4/3) * π * r^3
Given that the volume of the water in the tank is 7,500 ft^3, we can plug this value into the formula and solve for the radius:
7,500 = (4/3) * π * r^3
r^3 = (3/4) * (7,500 / π)
r = (3/4 * 7,500 / π)^(1/3)
r ≈ 9.67 ft
Once we have the radius of the tank, we can find the diameter by multiplying the radius by 2:
Diameter = 2 * radius
Diameter = 2 * 9.67 ft
Diameter ≈ 19.34 ft
Therefore, the diameter of the tank is approximately 19.34 feet.