When the temperature of a copper penny is increased by 100oC and its diameter increases by 0.17%. The area of one of its faces increases by

  1. 0.17%
  2. 0.51%
  3. 0.34%
  4. 0.085%
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Correct Option: (C)

\[ \mathrm{A = \pi r^{2}} \]

\[ \mathrm{A = \pi \left( \frac{d}{2} \right)^{2} = \frac{\pi d^{2}}{4}} \]

\[ \mathrm{\Delta A = \frac{\pi}{4} \ 2d \Delta d} \]

\[ \mathrm{\frac{\Delta A}{A} = \frac{\pi}{4} \ 2d \Delta d \ ÷ \ \frac{\pi d^{2}}{4}} \]

\[ \mathrm{\frac{\Delta A}{A} = 2\times \frac{\Delta d}{d}} \]

\[ \mathrm{\frac{\Delta A}{A} = 2\times 0.17 \%} \]

\[ \mathrm{\frac{\Delta A}{A} = 0.34 \%} \]


When the temperature of a copper penny is increased by 100oC and its diameter increases by 0.17%. The area of one of its faces increases by

When the temperature of a copper penny is increased by 100oC and its diameter increases by 0.17%. The area of one of its faces increases by

Correct Option: (C)

\[ \mathrm{A = \pi r^{2}} \]

\[ \mathrm{A = \pi \left( \frac{d}{2} \right)^{2} = \frac{\pi d^{2}}{4}} \]

\[ \mathrm{\Delta A = \frac{\pi}{4} \ 2d \Delta d} \]

\[ \mathrm{\frac{\Delta A}{A} = \frac{\pi}{4} \ 2d \Delta d \ ÷ \ \frac{\pi d^{2}}{4}} \]

\[ \mathrm{\frac{\Delta A}{A} = 2\times \frac{\Delta d}{d}} \]

\[ \mathrm{\frac{\Delta A}{A} = 2\times 0.17 \%} \]

\[ \mathrm{\frac{\Delta A}{A} = 0.34 \%} \]

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