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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. - CBSE Class 9 - Mathematics

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Question

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. 

Solution

Given that, let height →h say 

Height of `1^(st)` cone = h 

Height of `2^(nd)`cone = 3h 

Let the ratio of radii be r 

∴ Radius of `1^(st)`  cone=3r  

Radius of` 2 ^(nd)` cone = r 

∴ ratio of volume =` V_1/V_2` 

⇒ `V_1/V_2=(1/3pir_1^2h_1)/(1/3pir_2^2h_2)=(r_1^2h_1)/(r_2^2h_2)` 

=`((3r)^2xxh)/(r^2xx3h)`

`=(9r^2h)/(3r^2h)` 

= 3/1 

⇒  `v_1/v^2=3/1`

 

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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 20: Surface Areas and Volume of A Right Circular Cone
Ex.20.20 | Q: 3 | Page no. 21
Solution 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. Concept: Surface Area of a Right Circular Cone.
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