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(D) Let $r$ be the radius of the sphere.The surface area of a sphere is given by $4 \pi r^2$.Given,$4 \pi r^2 = 154$.$r^2 = \frac{154}{4 \pi} = \frac{

Vedclass · Accepted Answer

$179 \frac{2}{3} \, cm^3$

Vedclass · Answer

(D) Let $r$ be the radius of the sphere.The surface area of a sphere is given by $4 \pi r^2$.Given,$4 \pi r^2 = 154$.$r^2 = \frac{154}{4 \pi} = \frac{154 	imes 7}{4 	imes 22} = \frac{7 	imes 7}{4} = \left(\frac{7}{2}ight)^2$.Therefore,$r = \frac{7}{2} \, cm$.Now,the volume of the sphere is given by $V = \frac{4}{3} \pi r^3$.$V = \frac{4}{3} 	imes \frac{22}{7} 	imes \left(\frac{7}{2}ight)^3 \, cm^3$.$V = \frac{4}{3} 	imes \frac{22}{7} 	imes \frac{7}{2} 	imes \frac{7}{2} 	imes \frac{7}{2} \, cm^3$.$V = \frac{11 	imes 7 	imes 7}{3} \, cm^3 = \frac{539}{3} \, cm^3 = 179 \frac{2}{3} \, cm^3$.Thus,the required volume of the sphere is $179 \frac{2}{3} \, cm^3$.

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

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