Chapter 11.7, Problem 22PPS

a.

To determine

To calculate the distance travelled by the motorcycle in one rotation of a tire, rounded to the nearest tenth.

Answer to Problem 22PPS

  $19.4$ feet

Explanation of Solution

Given information: 1 mile $=5280$ feet and number of rotations made by tire to complete 1 mile $=272.5$ rotations.

Divide the number of feet covered in 1 mile by the number of rotations made to cover 1 mile.

  $\frac{5280}{272.5}$

On simplifying the expression.

  $=19.38$

Rounding of to the nearest tenth.

  $=19.4$ feet.

b.

To determine

To compute the height a tire, rounded to the nearest tenth.

Answer to Problem 22PPS

  $6.2$ feet

Explanation of Solution

Given information:As calculated in sub-part a., the distance covered by 1 revolution of a tire is $19.4$ feet. This is the circumference of the tire. Also, the diameter (d) denotes how tall the tire is.

Formula used: Circumference (c) of a circle can be calculated using formula $c=2\times \pi \times \frac{d}{2}$

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

Calculation:

  $c=2\times \pi \times \frac{d}{2}$

Formula for circumference of a circle.

or, $d=\frac{c}{\pi }$

Dividing 2 on both the numerator and denominator, and moving ‘d’ on the right-hand side of the equation.

  $=\frac{19.4\times 7}{22}$

Simplifying the expression.

  $=6.17$

Rounding off to the nearest tenth.

  $=6.2$ feet.