Answer: V ≈ 113.04 cubic meters
Step-by-step explanation: We know that the formula for the surface area of a sphere is:
SA = 4πr²
We are given that the surface area of this sphere is 113.04 square meters, so we can set up an equation:
113.04 = 4πr²
To solve for r, we need to isolate it. First, we can divide both sides by 4π:
113.04 ÷ 4π = r²
Simplifying:
r² ≈ 9.013
To solve for r, we can take the square root of both sides:
r ≈ 2.999
Now that we know the radius of the sphere is approximately 3 meters, we can use the formula for the volume of a sphere to find the volume:
V = (4/3)πr³
Substituting our value for r:
V = (4/3)π(2.999)³
Simplifying and rounding to the nearest hundredth:
V ≈ 113.04 cubic meters
Hope that helped!