Q2 of 13 Page 204

The base radii of two cylinders of the same height are in the ratio 3 : 4. What is the ratio of their volumes?

Given: ratio of radius of 2 cylinders is 3 : 4 ie. r1:r2

Height of the 2 cylinder is equal ie. h1=h2


To find : ratio of the volumes of the 2 cylinders ie. V1:V2



Procedure :


Volume of the cylinder = area of base × height


So, Volume of the cylinder = ∏×r2×h


⇒ Volume of the first cylinder V1= ∏×(r1)2×h1


⇒ Volume of the second cylinder V2= ∏×(r2)2×h2


So ratio of the volumes of these 2 cylinders =


⇒ =


=


= ×


= (2 ×


= ()2× 1


=


∴ =


∴ the ratio of the volumes of both the cylinders is 9:16 ie. V1:V2


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