Question

If radius of sphere is doubled, what is the ratio of volume of original sphere to that of second?

• A. $1:4$
• B. $8:1$
• C. $1:8$
• D. None

Answer 1

Answer: (C)

$1:8$

Given, radius of a sphere is doubled, i.e. $r=2r$

Volume of sphere $=\frac{4}{3}\pi r^3$ (original)
Vol of new sphere $=\frac{4}{3}\pi {\left(2r\right)}^3=\frac{4}{3}\pi {\left(8\right)r}^3$
Volume of original sphere / vol. of second sphere $=\frac{4/3\pi r^3}{4/3\pi r^3\left(8\right)}=\frac{1}{8}$