Answer:
42.84 inches.
Step-by-step explanation:
To find the diameter of a sphere with a volume of 78006 cubic inches, we can use the formula for the volume of a sphere, which is:
V = (4/3) * π * r^3
Where V is the volume of the sphere, π is the mathematical constant pi (approximately 3.14), and r is the sphere's radius.
First, we can rearrange the formula to solve for the radius:
r^3 = (3/4) * V / π
r = (3/4) * V / π^(1/3)
Substituting the given volume of 78006 cubic inches:
r = (3/4) * 78006 in^3 / π^(1/3)
r ≈ 21.42 inches (rounded to two decimal places)
Finally, we can find the diameter of the sphere by doubling the radius:
d = 2 * r
d ≈ 42.84 inches (rounded to two decimal places)
The diameter of a sphere with a volume of 78006 cubic inches is approximately 42.84 inches.