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in Surface Areas And Volumes by (26.9k points)
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A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is :

A. 1 : 2 : 3 

B. 2 : 1 : 3 

C. 2 : 3 : 1 

D. 3 : 2 : 1

1 Answer

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Best answer

Option : (A)

Volume of a hemisphere = \(\frac{2}{3}\)πr3 

Volume of a right circular cone = \(\frac{1}{3}\)πr2

Volume of a cylinder = πr2h

Given,

a cone, a hemisphere and a cylinder stand on equal bases and have the same height.

Height of a hemisphere is the radius and equal bases implies equal base radius. 

Thus, 

height of cone = height of cylinder = base radius = r

Ratio of volumes = \(\frac{1}{3}\)πr2h : \(\frac{2}{3}\)πr3 : πr2

⇒ Ratio of volumes = r3 : 2r3 : 3r3 

= 1 : 2 : 3

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