Question

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 1

Solution

r= radius

d= diameter

A= initial area

B=final area of the coin after it has expanded

1) Initial Area in terms of diameter

pi*r^2= A

pi*(D/2)^2 = A

(pi/4)*D^2= A

2) Final Area of the Coin

(pi/4)*(D + .0017D)^2= B [the diameter increases by .17 percent hence the "D+.0017D"]

(pi/4)*(1.0017D)^2= B

(pi/4)* D^2*1.003402= B

A* 1.003402 = B

3) B is 1.003402 times greater than a

hence the final area of the coin has increased by .34%