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# 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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ConceptVolume of a Sphere

#### 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^2hor

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

Or 1:2:3

Is there an error in this question or solution?

#### 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
Ex.21.20 | Q: 30 | 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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