Chapter 11.7, Problem 3CYP

To determine

To compare the circumferences of the two discs.

Answer to Problem 3CYP

  $2:1$ is the comparison of the circumferences.

Explanation of Solution

Given information: Diameter of larger disc(D) is $120$ millimeters.

Diameter of smaller disc(d) is $60$ millimeters.

Formula used: Circumference (c) of a circle can be calculated using formula $2\times \pi \times \frac{d}{2}$ and $2\times \pi \times \frac{D}{2}$ where ‘D’ and ‘d’ are the diameters of the two respective circles.

Calculation:

  $c_1=2\times \pi \times \frac{d}{2}$ , $c_2=2\times \pi \times \frac{D}{2}$

Formulae to compute the circumferences of the 2 discs.

  $c_2=2\times \pi \times \frac{D}{2}$

Computing circumference of the disc with larger diameter.

  $=2\times \pi \times \frac{120}{2}$

Simplifying the expression.

  $=120\pi$ millimeters.

  $c_1=2\times \pi \times \frac{d}{2}$

Computing circumference of the disc with smaller diameter.

  $=2\times \pi \times \frac{60}{2}$

Simplifying the expression.

  $=60\pi$ millimeters.

Comparing the two circumferences, take the ratio of the larger disc to the smaller disc.

  $\frac{c_2}{c_1}$$=\frac{120\pi }{60\pi }$

  $=2:1$ This is the comparison.