- 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 circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.

Given:

The circumference of two circles are in the ratio 2 : 3.

To do:

We have to find the ratio of their areas.

Solution:

Let the radius of the two circles be $r_1$ and $r_2$.

We know that,

Circumference of a circle of radius $r=2 \pi r$

Area of a circle of radius $r=\pi r^2$

Therefore,

Ratio of the circumference of the circles $=2 \times \frac{22}{7} \times r_1:2 \times \frac{22}{7} \times r_2$

$r_1:r_2=2:3$

Ratio of the areas of the circles $=\frac{22}{7} \times(r_1)^{2}:\frac{22}{7} \times(r_2)^{2}$

$=r_1^2:r_2^2$

$=(\frac{r_1}{r_2})^2$

$=(\frac{2}{3})^2$

$=\frac{4}{9}$

The ratio of the areas of the circles is $4:9$.

- Related Articles
- The diameters of two silver discs are in the ratio 2:3 . What Will be the ratio of their areas
- The ratio of the diameters of two circles is $3:4$, then find the ratio of their circumferences.
- The ratio between the areas of two circles is 16:9. Find the ratio between their radii, diameters and circumferences.
- The circumferences of two circles are in the ratio $5:7$, find the ratio between their radii.
- 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 ratio of radii of two cylinders is 1:2 and the heights are in the ratio 2:3. The ratio of their volumes is_____.
- 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 $4 : 3$.
- 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 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 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.
- Two circular cylinders of equal volumes have their heights in the ratio $1 : 2$. Find the ratio of their radii.
- Volumes of two spheres are in the ratio $64:27$. Find the ratio of their surface area.
- An archery target has three regions formed by three concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions."\n
- In two isosceles triangles, the angles opposite to their bases are equal and the ratio of their areas is \( 36: 25 \). Find the ratio of the corresponding altitudes of those triangles.
- The diameters of two cones are equal. If their slant heights are in the ratio $5 : 4$, find the ratio of their curved surfaces.

Advertisements