- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# The radii of two cylinders are in the ratio $2 : 3$ and their heights are in the ratio $5:3$. Calculate the ratio of their volumes and the ratio of their curved surfaces.

The radii of two cylinders are in the ratio $2 : 3$ and their heights are in the ratio $5:3$.

To do:

We have to find the ratio of their volumes and the ratio of their curved surfaces.

Solution:

Ratio in radii of two cylinders $= 2:3$

Ratio in their heights $= 5:3$

Let the radius of the first cylinder $(r_1) = 2x$ and the radius of the second cylinder $(r_2) = 3x$

Height of the first cylinder $(h_1) = 5y$ and the height of the second cylinder $(h_2) = 3y$

Volume of the first cylinder $= \pi r^2h$

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

$= 20\pi x^2y$

Volume of the second cylinder $= \pi (3x)^2 \times 3y$

$= 27\pi x^2y$

Ratio in their volumes $= 20\pi x^2y : 27\pi x^2y$

$= 20 : 27$

Curved surface area of the first cylinder $= 2\pi rh$

$= 2\pi \times 2x \times 5y$

$=20\pi xy$

Curved surface area of the second cylinder = 2\pi \times 3x \times 3y$

$= 18\pi xy$

Therefore,

Ratio in their curved surface areas $= 20\pi xy : 18\pi xy$

$= 10 : 9$

- Related Articles
- The ratio of radii of two cylinders is 1:2 and the heights are in the ratio 2:3. The ratio of their volumes is_____.
- Two cones have their heights in the ratio $1 : 3$ and the radii of their bases in the ratio $3:1$. Find the ratio of their volumes.
- Two circular cylinders of equal volumes have their heights in the ratio $1 : 2$. Find the ratio of their radii.
- The ratio of volumes of two cones is $4 : 5$ and the ratio of the radii of their bases is $2:3$. Find the ratio of their vertical heights.
- The diameters of two cones are equal. If their slant heights are in the ratio $5 : 4$, find the ratio of their curved surfaces.
- The ratio of radii of two cylinders is 1:2. If the ratio of their height is 2:1, then what will be the ratio of their volumes?
- The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.
- The circumferences of two circles are in the ratio $5:7$, find the ratio between their radii.
- Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio $4 : 3$.
- A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio $3:1$.
- Volumes of two spheres are in the ratio $64:27$. Find the ratio of their surface area.
- The ratio of the radii of two wheel is 2:5. What is the ratio of their circumferences ?
- The diameters of two silver discs are in the ratio 2:3 . What Will be the ratio of their areas
- Two isosceles triangles have equal vertical angles and their areas are in the ratio $36:25$. Find the ratio of their corresponding heights.
- The ratio of the diameters of two circles is $3:4$, then find the ratio of their circumferences.