A spherical water tank holds 10,500 ft^3 of water. What is the diameter of the tank? Upper V equals StartFraction pi Over 6 EndFraction d cubed
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To find the diameter of the spherical tank, we first need to calculate the volume of the sphere using the formula:
V = (4/3)πr^3
Given that the spherical water tank holds 10,500 ft^3 of water, we can set up the equation:
10,500 = (4/3)πr^3
Solving for r:
r^3 = (3/4)(10,500/π)
r^3 = 7,875
r ≈ 19.44 ft
Now that we have found the radius of the sphere, we can calculate the diameter which is equal to 2 times the radius:
d = 2r
d = 2(19.44)
d ≈ 38.87 ft
Therefore, the diameter of the spherical water tank is approximately 38.87 feet.