Area Expansion | MCQs

Explanation

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.

Let’s denote:

• Original diameter: $D$
  

• Increased diameter: $D' = D + Delta D = D (1 + 0.0017)$

• Area of a circle: $\mathrm{<br>}$

• New area:

  A′=π(D′)^2​/4=(D(1+0.0017))^2/4π​=A⋅(1+0.0017)^2

Use binomial expansion (for small x):

(1+x)^2≈1+2xwhen x is small

Here, $x=0.0017$, so:

(1+0.0017)^2≈1+2(0.0017)=1+0.0034=1.0034

Thus, the area increases by:

0.34%​