Final answer:
The volume of the sphere is provided as 1372/3π cubic inches. Using the sphere volume formula, we calculate the radius and find it to be 7 inches.
Therefore, the diameter of the sphere is 14 inches.
Step-by-step explanation:
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 of the sphere.
If we are given that the volume of the sphere is 1372/3π cubic inches, we can solve for the radius by setting this equal to the volume formula:
V = (4/3) π r^3
1372/3π = (4/3) π r^3
1372/3 = (4/3) r^3
We can divide both sides by 4/3 to solve for r^3:
r^3 = (1372/3) / (4/3)
r^3 = 343
Then we take the cube root of both sides to find the radius:
r = ∛343
r = 7 inches
Since the diameter is twice the radius, we can find the diameter by multiplying the radius by 2:
diameter = 2r
diameter = 2 × 7 inches
Diameter = 14 inches