​If the radius of a sphere is doubled, what will be the ratio of the volume of the new sphere to that of the original sphere?​

Correct option is A

Given:

The radius of the original sphere is r

The radius of the new sphere is 2r (doubled).

Solution:

Volume of the original sphere:

​$$v_1= \frac{4}{3}\pi r^3$$ 

​Volume of the new sphere:

​$$v_2= \frac{4}{3} \pi(2r)^3 = \frac{4}{3}(8r^3) = 8(\frac{4}{3} \pi r^3)$$ 

​Ratio of the volumes:

Ratio = $$\frac{V_2}{V_1}$$ = $$\frac{8(\frac{4}{3} \pi r^3)}{\frac{4}{3} \pi r^3}$$ = 8 : 1

​The ratio of the volume of the new sphere to that of the original sphere is 8 : 1.​