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