Chapter 11.7, Problem 17PPS

To determine

To compare the circumferences of the two discs.

Answer to Problem 17PPS

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

Explanation of Solution

Given information:

Diameter of larger disc(D) is

  $=2\frac{1}{2}or,\frac{5}{2}$ inches.

Diameter of smaller disc(d) is

  $=1\frac{1}{4}or,\frac{5}{4}$ inches.

For calculations, value of $\pi =\frac{22}{7}$ .

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:

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

Formula to calculate the circumference.

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

Computing circumference of the disc with larger diameter.

  $=2\times \pi \times \frac{5}{2\times 2}$

Simplifying the expression

  $=\frac{5\pi }{2}$ inches.

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

Computing circumference of the disc with smaller diameter.

  $=2\times \pi \times \frac{5}{2\times 4}$

Simplifying the expression.

  $=\frac{5\pi }{4}$ inches.

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

  $\frac{c_2}{c_1}$

Comparing the circumferences.

  $=\frac{\frac{5\pi }{2}}{\frac{5\pi }{4}}$

Simplifying the expression.

  $=\frac{5\pi \times 4}{2\times 5\pi }$

Dividing the common variables from the numerator and denominator.

  $\frac{4}{2}=\frac{2}{1}or2:1$

This is the comparison.