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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.2 in Chapter 17 - Mensuration
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The ratio of the heights of two right circular cones is 5 : 2 and that of their base radii is 2 : 5.
Find the ratio of their volumes.
Answer:
Solution:
Consider a cone with a height of "h" and a circular base with radius "r." This cone's volume will be equal to one-third of the base's area multiplied by its height.
Let h1 and h2 be the heights of the given cones and r1 and r2 be their radii.
Ratio of heights, h1:h2 = 5:2
Ratio of radii, r1:r2 = 2:5
Volume of cone, V1 = (1/3)π r12h1
Volume of cone, V2 = (1/3)π r22h2
V1 /V1 = (1/3)π r12h1/ (1/3)π r22h2
= r12 h1/ r22 h2
= 22×5/52×2
= 4×5/25×2
= 20/50 = 2/5
Hence the ratio of the volumes is 2:5.
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