the volume of a sphere is 5000 pi m^3. what is the surface area of the sphere to the nearest square meter?

Question

a) 4451 m^2
b) 3033 m^2
c) 1516 m^2
d) 888 m^2

Answer 1

To find the surface area of a sphere, we use the formula:

Surface Area = 4πr^2

where r is the radius of the sphere.

To find the radius of the sphere, we use the formula:

Volume = (4/3)πr^3

5000π = (4/3)πr^3

r^3 = (3/4)5000

r^3 = 3750

r ≈ 15.59 m (rounded to 2 decimal places)

Now we can use the surface area formula:

Surface Area = 4πr^2

Surface Area = 4π(15.59)^2

Surface Area ≈ 3033 m^2

Therefore, the answer is b) 3033 m^2 (rounded to the nearest square meter).