The volume of a sphere is 5000 π m3. What is the lateral surface area of the sphere to the nearest square meter?

1 answer

We can use the formula for the volume of a sphere:

V = (4/3)πr^3

where r is the radius of the sphere. Rearranging the formula, we get:

r^3 = (3V)/(4π)

We can then solve for r:

r = [(3V)/(4π)]^(1/3)

Plugging in V = 5000π, we get:

r = [(3 × 5000π)/(4π)]^(1/3) ≈ 16.08 m

The lateral surface area of the sphere is given by:

A = 4πr^2

Plugging in r ≈ 16.08, we get:

A ≈ 3233.95 m^2

Rounding to the nearest square meter, the lateral surface area is:

A ≈ 3234 m^2