Chapter 0.7, Problem 15E

To determine

To calculate: The distance travelled in 10 rotations by tire of 10-speed bicycle with diameter $\text{27 inches}$ .

Answer to Problem 15E

The distance covered in 10 rotations by the tire of 10-speed bicycle is $\text{848}\text{.5 inches}$ .

Explanation of Solution

Given information:

The tire for a 10-speed bicycle has a diameter of $\text{27 inches}$ .

Formula used:

Circumference $\left(C\right)$ of a circle with diameter d is given by $C=\pi d$ .

For each rotation of the tire, distance covered by wheel is equal to the circumference of the tire.

Calculation:

Consider the given statement that the tire for a 10-speed bicycle has a diameter of $\text{27 inches}$ .

Recall that the circumference $\left(C\right)$ of a circle with diameter d is given by $C=\pi d$ .

Apply it,

  $\begin{array}{c}C=\frac{\text{22}}{\text{7}}\text{×27 inches}\\ \text{=84}\text{.85 inches}\end{array}$

Now, recall that for each rotation of the tire, distance covered by wheel is equal to the circumference of the tire.

So, the distance covered in 10 rotations will be evaluated when $84.85$ is multiplied by 10.

So, the distance(d) covered in 10 rotations is calculated as,

  $\begin{array}{c}\text{d}=84.85\times 10\\ =848.5\end{array}$

Rounding off to the nearest tenth, we get,

  $\text{d=848}\text{.5 inches}$

Thus, the distance covered in 10 rotations by the tire of 10-speed bicycle is $\text{848}\text{.5 inches}$ .