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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

ConceptSurface Area of a Right Circular Cone

#### 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

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: 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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