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A thin square metal plate has side of le...

A thin square metal plate has side of length `l_(0)`. When the temperature of the plate is raised from `0^(@)C " to " 100^(@)C`, its length increased by 1%. What is the percentage increase in area of the plate in this case?

Text Solution

Verified by Experts

At `100^(@)C`, the length of a side of the square metal plate, `l=l_(0) times 101/100`
`therefore " " l^(2)=l_(0)^(2)(101/100)^(2)`
`therefore` The area of the metal plate at `100^(@)C`,
`" "A=A_(0)(101/100)^(2)" " [A_(0)=" area of the plate at " 0^(@)C]`
`therefore` Increase in area,
`DeltaA=A-A_(0)=A_(0)(101/100)^(2)-A_(0)`
`" " A_(0)/(100)^(2)[(101)^(2)-(100)^(2)]=201/(100)^(2)*A_(0)`
`therefore` Percentage increase,
`(DeltaA)/A_(0) times 100 =201/(100)^(2) times 100=2.01`
`therefore` Increase in area of the plate = 2.01%
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