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A metal half 11cm in radius is beated fr...

A metal half `11cm` in radius is beated from `10^(@)C to 80^(@)C` calculate the increase in surface area of the hall given coefficient of linear expansion of metal hall is `0.000017k^(-1)`

Text Solution

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Here `r_(10) = 11cm Delta T = 80 - 10 = 70^(@)C = 70 K`
`alpha = 0.000017 K^(-1) : beta = 2 alpha = 2 xx 0.000017 K^(-1)`
`S_(10) = 4 pi (r_(10))^(2) = 4 pi xx (11)^(2)`
increase in surface area
`Delta S = S_(10) beta Delta T = 4 pi xx (11)^(2) xx (2 xx 0.000017) xx 70`
`= 4 xx (22)/(7) xx 121 xx 0.000034 xx 70`
`= 3.62 cm^(2)`
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