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Question

Find the volume of a sphere whose surface area is $$154\ \text{cm}^2.$$


Solution

Let the radius of the sphere be $$r.$$

Surface area $$=154\ cm^2$$
             $$4\pi r^2=154$$
    $$4\cdot \dfrac{22}{7}\cdot r^2=154$$
                  $$r^2=\dfrac{154\times 7}{22\times 4}$$
                       $$=12.25$$
                    $$r=3.5\ cm$$


Volume of sphere $$=\dfrac{4}{3}\pi r^3$$
                               $$=\dfrac{4}{3}\times\dfrac{22}{7}\times 3.5\times 3.5\times 3.5$$
                               $$=179.67\ cm^3$$

Hence, the volume of the sphere is equal to $$179.67\ cm^3.$$

Mathematics

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