The volume of a sphere is 38808 cm³; find its diameter and the surface area.

Given,

Volume of the sphere = 38808 cm³

Let the radius of the sphere = r

By formula,

Volume of sphere = $\dfrac{4}{3}πr^3$

$\Rightarrow \dfrac{4}{3} πr^3 = 38808 \\[1em] \Rightarrow \dfrac{4}{3} \times \dfrac{22}{7} \times r^3 = 38808 \\[1em] \Rightarrow r^3 = \dfrac{(38808 \times 7 \times 3)}{(4 \times 22)} \\[1em] \Rightarrow r^3 = \dfrac{814968}{88} \\[1em] \Rightarrow r^3 = 9261 \\[1em] \Rightarrow r = \sqrt[3]{9261} \\[1em] \Rightarrow r = 21 \text{ cm}.$

∴ Diameter = 2r = 21 x 2 = 42 cm.

Surface area = 4πr² = $4 \times \dfrac{22}{7} \times 21 \times 21$

= 5544 cm².

Hence, diameter of ball = 42 cm and surface area = 5544 cm².