The spherical water tank with a volume of 7,500 ft³ has a diameter of approximately 24.28 feet.
We can find the diameter of the spherical water tank using the given volume (7,500 ft³) and the formula for the volume of a sphere:
Volume (V) = (4/3)πr³
where:
V is the volume of the sphere
π (pi) is a mathematical constant approximately equal to 3.14159
r is the radius of the sphere
Step 1: Relate diameter and radius
The diameter (d) is twice the radius (r):
d = 2r
Step 2: Substitute and solve for radius
We know the volume (V) and want to find the diameter (d), so we need to solve the formula for r:
r = ³√(V / [(4/3)π])
Plugging in the known volume (7,500 ft³):
r = ³√(7,500 ft³ / [(4/3)π])
r ≈ 12.14 ft
Step 3: Calculate diameter
Using the relationship between diameter and radius:
d = 2r ≈ 24.28 ft
Therefore, the diameter of the spherical water tank is approximately 24.28 feet