Question

The radii of two cylinders are in the ratio $2:3$ and their heights are in the ratio $5:3$. then what is the ratio of their volumes ?

• A. $10:17$
• B. $20:27$
• C. $10:27$
• D. $20:37$

Answer 1

Answer: (B)

$20:27$

Given radii ratio is $2:3$ and height ratio $5:3$

Let the radius be $2x,3x$ and height be $5y,3y$

$V_1=\pi (2x{)}^2\times 5y$

$V_2=\pi (3x{)}^2\times 3y$

$\frac{V_1}{V_2}=\frac{\pi (2x{)}^2\times 5y}{\pi (3x{)}^2\times 3y}=\frac{20}{27}$.