Question #5f791

1 Answer
Bishnu Paneru
Nov 12, 2015

Ratio of the volume of the cylinder, hemisphere and cone =
3:2:1

Explanation:

The circular base of the hemisphere fits in base of the cylinder and the radius of the hemisphere is equal to the height of the cylinder. The radius and height of the cone is equal.
Let height of the cone and cylinder, radius of the cylinder, cone and the hemisphere is r.
The volume of the cylinder = #Pi# #r^2#h = #Pi##r^2#Xr= #Pi##r^3#
Volume of the hemisphere = #1/2X4/3# #Pi# #r^3# = #2/3# #Pi# #r^3#
[ Volume of a sphere = #4/3# #Pi# #r^3#]
Volume of the cone = #1/3# #Pi# #r^2#h = #1/3# #Pi# #r^2#Xr = #1/3# #Pi# #r^3#

The ratio of the volume of the cylinder, hemisphere and cone
= #Pi##r^3# : #2/3# #Pi# #r^3# : #1/3# #Pi# #r^3#
Cancelling #Pi# #r^3# from all three proportionals we get,
= 1 : #1/3# : #2/3#
= 3X1 : 3X#1/3# : 3X#2/3# [multiplying by 3]
= 3 : 2 : 1

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