- 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 ratio between the areas of two circles is 16:9. Find the ratio between their radii, diameters and circumferences.

**Given : **

Ratio between areas of two circles = 16 : 9

**To Find : **

i) Ratio between radii of circles.

ii) Ratio between diameters of circles

iii) Ratio between circumferences of circles

**Solution :**

Lets take Circle 1 and Circle 2

Radius of Circle 1 = r _{1 }

Radius of Circle 2 = r _{2 }

Diameter of Circle 1 = d _{1 }

Diameter of Circle 2 = d _{2}

Area of circle 1 : Area of circle 2 = 16 : 9

Formula to find area of circle = π r ^{2 }

$\displaystyle \begin{array}{{>{\displaystyle}l}}

π\ r^{2}_{1} \ :π\ r^{2}_{2} \ =\ 16\ :\ 9\\

\\

\frac{π\ r^{2}_{1}}{π\ r^{2}_{2}} \ =\ \frac{16}{9}\\

\\

\frac{r^{2}_{1}}{r^{2}_{2}} \ =\ \frac{16}{9}\\

\\

\left(\frac{r_{1}}{r_{2}}\right)^{2} \ =\ \frac{16}{9}\\

\\

\ \ \frac{r_{1}}{r_{2}} \ =\ \sqrt{\frac{16}{9}} \ \\

\\

\ \ \frac{r_{1}}{r_{2}} \ \ =\ \ \frac{4}{3}\\

\\

r_{1} \ :\ r_{2} \ =\ 4\ :\ 3\\

\

\end{array}$

Ratio between radii of circles = 4 : 3

Diameter = 2 r

$\displaystyle \begin{array}{{>{\displaystyle}l}}

d_{1} \ =\ 2\times r_{1} \ \ \ \ ;\ d_{2} \ =\ 2\times r_{2}\\

\\

\frac{d_{1} \ }{d_{2} \ \ } \ =\ \frac{2\times r_{1}}{\ 2\times r_{2}}\\

\\

\frac{d_{1} \ }{d_{2} \ \ } \ =\ \frac{r_{1}}{\ r_{2}} \ \\

\\

\frac{d_{1} \ }{d_{2} \ \ } \ =\ \ \frac{4}{\ 3}\\

\\

d_{1} \ :\ d_{2} \ =\ 4\ :\ 3

\end{array}$

Ratio between Diameters of two circles = 4 : 3

Circumference of circle = 2πr

$\displaystyle \begin{array}{{>{\displaystyle}l}}

\ 2πr_{1} \ \ :\ 2πr_{2}\\

\\

\ \frac{2πr_{1}}{\ 2πr_{2}} \ =\ \frac{r_{1}}{\ r_{2}}\\

\\

\ \frac{2πr_{1}}{\ 2πr_{2}} \ =\ \ \frac{4}{\ 3}\\

\\

\ 2πr_{1} :2πr_{2} \ =\ 4\ :\ 3

\end{array}$

Ratio between circumferences of circles = 4 : 3

**i) Ratio between radii of circles = 4 : 3**

**ii) Ratio between diameters of circles = 4 : 3**

**iii) Ratio between circumferences of circles = 4 : 3**

- Related Articles
- The circumferences of two circles are in the ratio $5:7$, find the ratio between their radii.
- The ratio of the diameters of two circles is $3:4$, then find the ratio of their circumferences.
- The ratio of the radii of two wheel is 2:5. What is the ratio of their circumferences ?
- The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.
- The circumferences of the two concentric circles are $12\ cm$ and $72\ cm$. What is the difference between their radii?
- Ratio between the sides of two squares is 2: 5: find the ratio between their perimeter and area
- The diameters of two silver discs are in the ratio 2:3 . What Will be the ratio of their areas
- 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 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.
- 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 $4 : 3$.
- The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.
- Two circular cylinders of equal volumes have their heights in the ratio $1 : 2$. Find the ratio of 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_____.
- The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.