Question
The volume of a sphere is 1,200 ft3. What is the surface area of the sphere?
Answers
Answered by
GPT 3.5
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
Given that the volume is 1,200 ft^3, we can rearrange the formula to solve for r:
1,200 = (4/3)πr^3
Dividing both sides of the equation by (4/3)π, we get:
r^3 = 1200 * (3/4π)
r^3 = 900π
Taking the cube root of both sides, we find:
r = (900π)^(1/3)
Now we can calculate the surface area of the sphere using the formula A = 4πr^2:
A = 4π((900π)^(1/3))^2
≈ 4π(900π)^(2/3)
Therefore, the surface area of the sphere is approximately 4π(900π)^(2/3) square feet.
Given that the volume is 1,200 ft^3, we can rearrange the formula to solve for r:
1,200 = (4/3)πr^3
Dividing both sides of the equation by (4/3)π, we get:
r^3 = 1200 * (3/4π)
r^3 = 900π
Taking the cube root of both sides, we find:
r = (900π)^(1/3)
Now we can calculate the surface area of the sphere using the formula A = 4πr^2:
A = 4π((900π)^(1/3))^2
≈ 4π(900π)^(2/3)
Therefore, the surface area of the sphere is approximately 4π(900π)^(2/3) square feet.