Question

The volume of a cylinder is twice the volume of a sphere whose radius is twice the height of the cylinder. Then the ratio of the radius of the cylinder to the height is:

• A. 8 : √3
• B. 2 : √3
• C. √3 : 8
• D. 4 : √3

Answer 1

Answer:

A. 8 : √3

$V_c=\pi r^2h$

$V_s=\frac{4}{3}\pi r^3$

$V_c=2V_s$

radius of cylinder = 2h

$\pi r^2h= 2 \times \frac{4}{3}\pi (2h)^3$

$r^2h=\frac{8}{3}\times 8h^3$

$r^2=\frac{64}{3} h^2$

$\frac{r^2}{h^2}=\frac{64}{3}$

$\frac{r}{h}=\sqrt{\frac{64}{3}}$

$\frac{r}{h}=\frac{8}{\sqrt{3}}$

$r:h=8:\sqrt{3}$