CTET 2 Math and Science Jan 2012 Paper

Question : 55 of 120

Marks: +1, -0

The diameter of a cylindrical jar is increased by 25%. By what percent must the height of the jar be decreased so that there is no change in its volume?

Validate

Solution:

Volume of cylinder

=πr^2h

r_{1}=r+r×\;\;{25}/{100}=\;\;{5r}/{4}

Let ‘h’ is decreased by x%

h_{1}=h-h×\;\;{x}/{100}=h(1-\;\;{x}/{100})

Now equality both the volume

πr^{2}h=π(\;\;{5r}/{4})^{2}(1-\;\;{x}/{100})h

⇒1=\;\;{25}/{16}×(1-\;\;{x}/{100})

⇒(1-\;\;{x}/{100})=(\;\;{4}/{5})^{2}

⇒1-\;\;{x}/{100}=\;\;{16}/{25}

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