Q. 3 A5.0( 1 Vote )

# The base radii of two cylinders are in the ratio 2 : 3 and their height are in the ratio 5 : 4.

What is the ratio of their volumes?

Answer :

Given: ratio of base radii of 2 cylinders is 2:3 ie. r_{1}:r_{2}

ratio of height of 2 cylinders is 5:4 ie. h_{1}:h_{2}

to find : i) ratio of the volumes of 2 cylinders

ii) volume of the second cylinder if first’s volume is 720cm^{3}

procedure :

i)Volume of cylinder = area of base × height

So, Volume of the cylinder = ∏×r^{2}×h

⇒Volume of the first cylinder V1= ∏×(r_{1})^{2}×h_{1}

⇒Volume of the second cylinder V2= ∏×(r_{2})^{2}×h_{2}

So ratio of the volumes of these 2 cylinders =

⇒ =

=

= ×

= (^{2} ×

= ()^{2}×

= ×

=

⇒ =

∴ ratio of volumes of 2 cylinders = 5:9 ie. V_{1}:V_{2}

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The base radii of two cylinders are in the ratio 2 : 3 and their height are in the ratio 5 : 4.

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