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Solution for A Cone, a Hemisphere and a Cylinder Stand on Equal Bases and Have the Same Height. Show that Their Volumes Are in the Ratio 1 : 2 : 3. - CBSE Class 9 - Mathematics

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Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

Solution

Given that,
A cone, hemisphere and a cylinder stand one equal bases and have the same weight
We know that

`V_"cone ": V_"hemispere" : V_"cylinder"`

⇒ `1/3πr^2h:2/3πr^3:πr^2h`

Multiplying by 3

⇒ ` π r^2 h : 2πr^3 : 3πr^2h`or

`πr^3 : 2πr^3 : 3πr^3 [∴ r=h ∵ r^2 h = r^3]`

Or 1:2:3 

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 21: Surface Areas and Volume of a Sphere
Q: 25 | Page no. 21
Solution A Cone, a Hemisphere and a Cylinder Stand on Equal Bases and Have the Same Height. Show that Their Volumes Are in the Ratio 1 : 2 : 3. Concept: Volume of a Sphere.
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