two cones have their height in ratios 1:3 and the radii of their bases are in ratio 3:1 .show that their volumes are in ratio 3:1.
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Shiv4225:
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height of the cone 1 = 1x
cone 2= 3x
Radius of the cone 1= 3y
cone 2 = 1 y
volume of the cone = (1/3) byr^2
volume of the cone 1= (1/3) by* 9y^2 x
volume of the cone 2 = (1/3) by* y^2 3x
(1/3) by* 9y^2 x / (1/3) by* y^2 3x = 9/3
=3/1
so ratio is 3:1
cone 2= 3x
Radius of the cone 1= 3y
cone 2 = 1 y
volume of the cone = (1/3) byr^2
volume of the cone 1= (1/3) by* 9y^2 x
volume of the cone 2 = (1/3) by* y^2 3x
(1/3) by* 9y^2 x / (1/3) by* y^2 3x = 9/3
=3/1
so ratio is 3:1
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