Question

The volume of a sphere is 4,000π m³. What is the surface area of the sphere to the nearest square meter?

a) 2,614 m²

b) 3,836 m²

c) 1,307 m²

d) 794 m²

Answer 1

The surface area of the sphere is approximately 2,614 m².

Step-by-step explanation:

To find the surface area of a sphere, you can use the formula A = 4πr², where A is the surface area and r is the radius of the sphere. In this case, the volume of the sphere is given as 4,000π m³. Since the volume is 4/3 πr³ and the radius cubed is proportional to the volume, we can solve for the radius by rearranging the equation: r³ = (3/4) (volume/π). Substituting the given volume of 4,000π m³, we get r³ = (3/4) (4,000π/π) = 3,000. Taking the cube root of both sides, we find that r = ∛(3,000) ≈ 14.48 m. Now we can substitute this radius into the surface area formula to get the surface area: A = 4π(14.48)² ≈ 2,614 m². Therefore, the correct answer is a) 2,614 m².