Final answer:
To find the radius of a sphere with a volume of 40 cubic inches using the formula V = 4/3 π r^3, we rearrange the formula and solve for r, resulting in a radius of approximately 1.7 inches.
Step-by-step explanation:
The volume of a sphere is given by the formula V = 4/3 π r^3. To find the radius of a sphere with a given volume, we can rearrange the formula to solve for r. If a sphere has a volume of 40 cubic inches, we can substitute V with 40 in the formula and solve for the radius (r).
To isolate r, we first multiply both sides by 3/4 and then divide by π:
3/4 × V = π r^3 → r^3 = (3/4 × V)/π
After substituting V with 40, we would then take the cube root of both sides of the equation to find the radius.
r = ∛((3/4 × 40)/π)
Using a calculator, this gives us:
r ≈ 1.7 inches
Therefore, the radius of a sphere with a volume of 40 cubic inches is approximately 1.7 inches.