Question

The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter? 165 m2 2,158 m2 1,079 m2 37,699 m2

Answer 1

To solve this problem and calculate the area of the sphere, you must apply the following formulas:

 Formula N° 1:

 V=4/3(πr³)  

 V is the volume of the sphere (V=3,000π m³).
 r is the radius.

 Formula N° 2:

 A=4πr²

 A is the area of the sphere.
 r is the radius.

 As you can see, you don't have the value of the radius "r". So, you must rewrite the Formula N° 1, and clear "r":

 V=4/3(πr³)
 (3,000)(3)=4πr²
 r³=9,000/4π
 r=(9,000/4π)^1/3
 r=13.1037 m

 Then, to calculate the area of the sphere, you must substitute the value of "r" into the Formula N° 2:

 A=4πr²
 A=4π(13.1037)²
 A=2,158 m²

 What is the surface area of the sphere to the nearest square meter?

 The answer is: 2,158 m²