When the temperature of a copper penny is increased by 100 °C, its diameter increases by 0.17%. The area of one of its faces increases by:

Answer: 0.34%

We are told:

A copper penny is heated to 100 °C.
Its diameter increases by 0.17%.
We are to find the percentage increase in the area of one of its circular faces.

Original diameter: $D$
Increased diameter: $D' = D + Delta D = D (1 + 0.0017)$
Area of a circle:
New area:
$A^{'} = π ( D ^{'} )^ ^{2} = ( D ( 1 + 0.0017 ) )^ ^{2/} = A \cdot (1 + 0.0017)^^{2}$

$(1 + x)^^{2} \approx 1 + 2 x when x is small$

Here, $x = 0.0017$ , so:

$(1 + 0.0017)^^{2} \approx 1 + 2 (0.0017) = 1 + 0.0034 = 1.0034$

Thus, the area increases by:

$0.34%$

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