- 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

# Volumes of two spheres are in the ratio $64:27$. Find the ratio of their surface area.

**Given:**Volumes of two spheres are in the ratio $64:27$.

**To do:**To find the ratio of their surface area.

**Solution:**

To find the ratio of the surface areas, first we have to find the surface areas with their volumes.

Radius of big sphere $=R$

Radius of small sphere $=r$

Volume of bigger sphere$=\frac{4}{3}\pi R^3$

Volume of smaller sphere$=\frac{4}{3}\pi r^3$

Given, Volume of bigger sphere$:$Volume of smaller sphere $=64:27$

$\Rightarrow \frac{\frac{4}{3}\pi R^3}{\frac{4}{3}\pi r^3}=\frac{64}{27}$

$\Rightarrow \frac{R^3}{r^3}=\frac{64}{27}$

$\Rightarrow \frac{R}{r}=\sqrt[3]{\frac{64}{27}}$

$\Rightarrow \frac{R}{r}=\frac{4}{3}$

Surface area of bigger sphere$=4\pi R^2$

Surface area of smaller sphere$=4\pi r^2$

Hence, Surface area of bigger sphere: Surface area of smaller sphere$=\frac{4\pi R^2}{4\pi r^2}$

$=( \frac{R}{r})^2$

$=( \frac{4}{3})^2$

Thus, the ratio of their surface areas $=16:9$

- Related Articles
- 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.
- Two circular cylinders of equal volumes have their heights in the ratio $1 : 2$. Find the ratio of their radii.
- 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.
- 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 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 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.
- Find the ratio of the total surface area and lateral surface area of a cube.
- 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 $4 : 3$.
- Ratio between the sides of two squares is 2: 5: find the ratio between their perimeter and area
- The diameters of two cones are equal. If their slant heights are in the ratio $5 : 4$, find the ratio of their curved surfaces.
- If the ratio of the sum of first n terms of two A.P’s is $( 7n\ +1)$: $( 4n\ +\ 27)$, find the ratio of their $m^{th}$ terms.
- If the ratio of the sum of the first n terms of two APs is $(7n + 1)$: $(4n + 27)$, then find the ratio of their 9$^{th}$ terms.
- The ratio of the diameters of two circles is $3:4$, then find the ratio of their circumferences.

Advertisements