Surface Areas and Volumes — Question 9

Let the radius of the sphere be r.

By formula,

Surface area of the sphere = 4πr²

Substituting values we get :

$\Rightarrow 4πr^2 = 154 \\[1em] \Rightarrow r^2 = \dfrac{154}{4π} \\[1em] \Rightarrow r^2 = \dfrac{154}{4 \times \dfrac{22}{7}} \\[1em] \Rightarrow r^2 = \dfrac{154 \times 7}{4 \times 22} \\[1em] \Rightarrow r^2 = \dfrac{49}{4} \\[1em] \Rightarrow r = \sqrt{\dfrac{49}{4}} \\[1em] \Rightarrow r = \dfrac{7}{2} \text{ cm}.$

By formula,

Volume of a sphere (V) = $\dfrac{4}{3}πr^3$

$V = \dfrac{4}{3} \times \dfrac{22}{7} \times \Big(\dfrac{7}{2}\Big)^3 \\[1em] = \dfrac{4}{3} \times \dfrac{22}{7} \times \dfrac{343}{8} \\[1em] = \dfrac{11}{3} \times 49 \\[1em] = \dfrac{539}{3} \\[1em] = 179 \dfrac{2}{3} \text{ cm}^3$

Hence, volume of the sphere is $179 \dfrac{2}{3} \text{ cm}^3$.