Question

The volume of a sphere is 2,254 pi m^3 what is the surface area of the sphere to the nearest tenth?

Answer 1

The answer is 567.4 π m².

The surface area of the sphere with radius r is: A = 4 π r²
The volume of the sphere with radius r is: V = 4/3 π r³

Step 1. Calculate the radius from the volume:
V = 4/3 π r³ = 2,254 π m³
r³ = (2,254 π) / (4/3 π)
r³ = 2,254 π/π * 3/4
r³ = 2,254 * 3/4
r³ = 1,690.5
r = ∛1,690.5
r = 11.91 m

Step 2. Calculate the surface area using the r:
A = 4 π r²
A = 4 π 11.91²
A = 567.4 π m²