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Question

On heating a uniform metallic cylinder length increases by 3%. The area of cross-section of its base will increase by

A
1.5%
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B
3%
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C
9%
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D
6%
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Solution

The correct option is C 9%
According to the question,
The area of the base is πr2 or πd24 where r is the radius and d is the diameter.
So, we have r or d both of have the dimension of length,
A=πr2
δA=3πr2×δr
=δAA
=3×(δrr)
So, it is given that δrr=3%
Hence,
δAA3×3%
=9%
So, the area of the cross- section of its base will increase by 9%.

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