Find the volume and surface area of a sphere of radius :

(i) 10.5 cm

(ii) 4.2 cm

(i) Given, r = 10.5 cm

Surface area of sphere = 4πr²

$= 4 \times \dfrac{22}{7} \times 10.5^2 \\[1em] = 4 \times \dfrac{22}{7} \times 110.25 \\[1em] = \dfrac{9702}{7} \\[1em] = 1386 \text{ cm}^2.$

Volume of sphere = $\dfrac{4}{3}$ πr³

$= \dfrac{4}{3} \times \dfrac{22}{7} \times 10.5^3 \\[1em] = \dfrac{4}{3} \times \dfrac{22}{7} \times 1157.625 \\[1em] = \dfrac{101871}{21} \\[1em] = 4851 \text{ cm}^3.$

Hence, volume of the sphere is 4851 cm³ and surface area of a sphere is 1386 cm².

(ii) Given, r = 4.2 cm

Surface area of sphere = 4πr²

$= 4 \times \dfrac{22}{7} \times 4.2^2 \\[1em] = 4 \times \dfrac{22}{7} \times 17.64 \\[1em] = \dfrac{1552.32}{7} \\[1em] = 221.76 \text{ cm}^2.$

Volume of sphere = $\dfrac{4}{3}$ πr³

$= \dfrac{4}{3} \times \dfrac{22}{7} \times 4.2^3 \\[1em] = \dfrac{4}{3} \times \dfrac{22}{7} \times 74.088 \\[1em] = \dfrac{6519.744}{21} \\[1em] = 310.464 \text{ cm}^3.$

Hence, volume of the sphere is 310.464 cm³ and surface area of a sphere is 221.76 cm².