Question

The volume, V, of a sphere in terms of its radius, r, is given by

V(r)= 4/3 πr^3 . Find the radius of a sphere, in feet, with a volume of 500 cubic feet. Use 3.14 for π and round your answer to the nearest hundredth.

a) 4.53 feet
b) 7.14 feet
c) 8.66 feet
d) 10.08 feet

Answer 1

To find the radius of a sphere with a volume of 500 cubic feet, we can use the formula for the volume of a sphere, V(r) = (4/3)πr^3. By substituting the known volume into the equation, we can solve for the radius.

Step-by-step explanation:

To find the radius of a sphere with a volume of 500 cubic feet, we can use the formula for the volume of a sphere, which is V(r) = (4/3)πr^3. We are given that the volume is 500 cubic feet, so we can substitute this value into the equation:

500 = (4/3)πr^3

To find the radius, we need to isolate it on one side of the equation. Divide both sides of the equation by (4/3)π:

r^3 = (500) / ((4/3)π)

Then, take the cube root of both sides to solve for r:

r = (500)^(1/3) / ((4/3)π)^(1/3)

Using the value of π as 3.14, we can substitute this value and calculate the radius rounded to the nearest hundredth:

r ≈ 4.53 feet