- 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 $4:9$.
Advertisements