- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

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

# If the triangle $ \mathrm{ABC} $ in the Question 7 above is revolved about the side $ 5 \mathrm{~cm} $, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8 .

Given:

A right triangle \( \mathrm{ABC} \) with sides \( 5 \mathrm{~cm}, 12 \mathrm{~cm} \) and \( 13 \mathrm{~cm} \) is revolved about the side \( 5 \mathrm{~cm} \).

To do:

We have to find the ratio of the volumes of the two solids obtained.

Solution:

Let in a triangle $ABC$,

$AB=13\ cm$

$BC=5\ cm$

$CA=12\ cm$

On revolving the right angled triangle $ABC$ about the side $BC$, we get a cone as shown in the below figure.

Therefore,

Height of the cone $h=5\ cm$

Radius of the cone $r=12\ cm$

We know that,

Volume of a cone of radius $r$ and height $h$ is $\frac{1}{3} \pi r^2h$

This implies,

Volume of the cone $=\frac{1}{3} \times \pi (12)^2 \times 5$

$=240\pi\ cm^3$

The volume of the cone so formed is $240\pi\ cm^3$.

The ratio of the volumes of the two solids so obtained $=100\pi\ cm^3:240\pi\ cm^3$$=100:240$

$=5:12$

The ratio of the volumes of the two solids so obtained is $5:12$.

- Related Questions & Answers
- Find coordinates of the triangle given midpoint of each side in C++
- What is the best answer to the question about your biggest weakness?
- Find sum of the series 1-2+3-4+5-6+7....in C++
- Program to find the Centroid of the Triangle in C++
- C++ program to find the Radius of the incircle of the triangle
- Why so mangrove roots grow above the ground?
- C++ program to find the side of the Octagon inscribed within the square
- Find the dimensions of Right angled triangle in C++
- What is so special about the great bath in Mohenjo-Daro?
- Program to find the Area and Volume of Icosahedron in C++
- Java program to find the area of a triangle
- Python Pandas - Check if the interval is open on the left side
- Python Pandas - Check if the interval is open on the right side
- Java Program to Find the Surface area and Volume of Cuboid
- Sum of the series 1 + (1+3) + (1+3+5) + (1+3+5+7) + + (1+3+5+7+....+(2n-1)) in C++
- Sum of the series 1 + (1+3) + (1+3+5) + (1+3+5+7) + ...... + (1+3+5+7+...+(2n-1)) in C++