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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. - CBSE Class 9 - Mathematics

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Question

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. 

Solution

Let ratio of radius be 'r '

Radius of `1^(st)`cone = 2r 

Radius of `2^(nd)`cone = 3r  

Similarly 

Let volume ratio be ‘v’ 

Volume of `1^(st)` cone→  4v  

Similarly volume of `2^(nd)` cone → 5v 

∴`V_1/V_2=(4v)/(5v)=4/5` 

⇒ `(1/3pir_1^2h_1)/(1/3pir_1^2)=4/5` 

⇒`( h_1(2r)^2)/(h_2(3r)^2)=4/5` 

⇒` h_1/h_2xx(4r^2)/(9r^2)=4/5` 

⇒ `h_1/h_2xx36/20=18/20=9/5` 

∴ Ratio of the inner height is 9:5 

  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 20: Surface Areas and Volume of A Right Circular Cone
Ex.20.20 | Q: 6 | Page no. 21
Solution 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. Concept: Surface Area of a Right Circular Cone.
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