Final answer:
To find the surface area of a sphere with a given volume of 3500π m³, first calculate the radius using the volume formula and then use the radius to compute the surface area with the formula A = 4πr². Upon calculation, the surface area appears to be approximately 7,415 m², but this does not match the given options.
Step-by-step explanation:
The volume of a sphere is given by Volume = (4/3) π r³. Since we know the volume of the sphere is 3,500π m³, we can solve for the radius (r) of the sphere:
3,500π = (4/3)π r³
Multiplying both sides by 3/4 to isolate r³ gives:
3,500π × (3/4) = π r³ =>
2,625π = π r³
Now, divide both sides by π:
2,625 = r³
To find r, take the cube root of both sides:
r = ∛(2,625) ≈ 13.76 m
We can now use the formula for the surface area of a sphere, which is A = 4πr².
Substituting the radius we found:
A = 4π(13.76 m)²
Calculating the surface area:
A ≈ 4π(189.57 m²) ≈ 4π(190 m²) ≈ 2,360π m²
Since π is approximately 3.14159, the surface area becomes:
A ≈ 2,360 × 3.14159 m² ≈ 7,415 m²
Rounding this to the nearest square meter, we get A ≈ 7,415 m².
Hence, none of the given options are correct.