Question

A cylinder circumscribes a sphere. What is the ratio of their volumes?

• A. $1:2$
• B. $3:2$
• C. $4:3$
• D. $5:6$

Answer 1

The correct option is B $3:2$

Let radius of sphere $=r$

Then, radius of cylinder $=r$

And height of cylinder $=r+r=2r$

$\therefore$ Required Ratio = $\frac{\pi r^{2}h}{\frac{4}{3}\pi r^3}=\frac{2r\times 3}{4\times r}=\frac{3}{2}\Rightarrow 3:2$