If the radius of a sphere is increased by 2.5 decimetre (dm), then its surface area increases by 110 dm². What is the volume (in dm³) of the sphere? $$\left( {{\text{take }}\pi = \frac{{22}}{7}} \right)$$

A. $$\frac{{13}}{{21}}$$

B. $$\frac{3}{7}$$

C. $$\frac{4}{7}$$

D. $$\frac{{11}}{{21}}$$

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & 4\pi \left[ {{{\left( {x + 2.5} \right)}^2} - {x^2}} \right] = 110 \cr & \Rightarrow 4 \times \frac{{22}}{7}\left[ {5x + 6.25} \right] = 110 \cr & \Rightarrow 20x = 10 \cr & \Rightarrow x = \frac{1}{2} \cr & \Rightarrow {\text{Volume}} = \frac{4}{3} \times \frac{{22}}{7} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{{11}}{{21}} \cr} $$