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If the surface area of a sphere is 1386 cm², what will be its volume?
Question

If the surface area of a sphere is 1386 cm², what will be its volume?

A.

1617 cm³

B.

3234 cm³

C.

4851 cm³

D.

9702 cm³

Correct option is C

If the surface area of a sphere is 1386 cm², what will be its volume?

Given:
-Surface Area of Sphere = 1386 cm²

Formula Used:

Surface Area of Sphere = 4πr²

Volume of Sphere = (4/3)πr³

Solution:

Use surface area formula to find radius (r):
4πr² = 1386
=>r2=1386(4π) =>r=(1386(4π))10.5cm=212=> r² = \frac{ 1386 }{ (4π)}\\\ \\=> r = \frac{√(1386 }{ (4π)}) ≈ 10.5 cm = \frac{21}{2} cm​
Use radius to find volume:
Volume = (43)πr3(\frac{4}{3})πr³​​
=> Volume ≈ (43)×π×(212×212×212) (\frac{4}{3}) × π × (\frac{21}{2}\times \frac{21}{2} \times \frac{21}{2})​​

=> Volume ≈  43×227×212×212×212\frac{4}{3} \times\frac{22}{7} \times \frac{21}{2}\times \frac{21}{2}\times \frac{21}{2}​​
Hence, the volume of the sphere is approximately 4851 cm³.

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