Final answer:
To find the radius of a sphere with a volume of 4500 cubic inches, we can rearrange the volume formula V = (4/3)πr³ to solve for r. After substituting the given volume and simplifying, the radius is approximately 10.61 inches.
Step-by-step explanation:
To find the radius of a sphere given its volume, we use the formula for the volume of a sphere, which is V = (4/3)πr³. We can rearrange this formula to solve for the radius, r, which involves using cube root and division.
First, we isolate r³ by multiplying both sides of the equation by 3/4 and then dividing by π:
r³ = (3V)/(4π)
Next, we take the cube root of both sides to solve for r:
r = ∛((3V)/(4π))
Given the volume of the sphere is 4500 cubic inches, we substitute that into the equation:
r = ∛((3 * 4500)/(4π))
Now, we can calculate the radius:
r ≈ ∛(3375/π)
r ≈ 10.61 inches
Therefore, the radius of the sphere is approximately 10.61 inches.