A spherical water tank holds 8,500 ft^3 of water. What is the diameter of the tank?
(Hint: V= pi / 6 d^3 written like pie over six... d to the 3rd power.
The diameter is ___ ft.
what, you have the hint, and don't use it?
π/6 d^3 = 8500
d^3 = 51000/π = 16233.8042
now just take the cube root to find d
To find the diameter of the spherical water tank, you can use the formula for the volume of a sphere:
V = (π/6) * (d^3)
Given that the tank holds 8,500 ft^3 of water, we can substitute this value into the formula:
8,500 = (π/6) * (d^3)
To solve for the diameter (d), we need to rearrange the equation to isolate d^3. Divide both sides of the equation by (π/6):
8,500 / (π/6) = d^3
Now, simplify the expression on the left side by multiplying by the reciprocal of (π/6), which is 6/π:
8,500 * (6/π) = d^3
Next, find the cube root of both sides of the equation to solve for d:
d = (8,500 * (6/π))^(1/3)
Calculating this expression, we get:
d ≈ 18.83 ft
Therefore, the approximate diameter of the tank is 18.83 ft.