What is the approximate volume of the sphere if the surface area is 482.8 mm²?
- 998 mm^2
- 1,126 mm^2
- 2,042 mm^2
- 2,993 mm^2
The volume of a sphere can be calculated using the formula:
V = (4/3)πr³
The surface area of a sphere is given by the formula:
A = 4πr²
We are given the surface area, A, as 482.8 mm². Therefore, we can solve for the radius, r, using the formula for surface area:
482.8 = 4πr²
r² = 482.8 / (4π)
r² ≈ 38.478
r ≈ √38.478
r ≈ 6.20 mm
Now we can calculate the volume using the formula for volume:
V = (4/3)πr³
V ≈ (4/3)π(6.20)³
V ≈ 2,042 mm³
Therefore, the approximate volume of the sphere is 2,042 mm³. Therefore, the correct answer is: 2,042 mm^2.