Q15. - Algebra 1

Question

The tire for a 10 -speed bicycle has a diameter of 27 inches. Find the distance traveled in 10 rotations of the tire. Round to the nearest tenth.

Step-by-Step Solution

Answer

The distance covered in 10 rotations by the tire of a 10-speed bicycle is 848.5 inches.

Step 1. Given information.

The tire for a 10-speed bicycle has a diameter of 27 inches.

Step 2. Circumference of a circle.

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

 

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

Step 3. Calculations.

The given statement is that the tire for a 10-speed bicycle has a diameter of 27 inches. So,

$$\begin{gathered} C=\frac{22}{7}\times 27\mathrm{inches} \\ =84.85\mathrm{inches} \end{gathered}$$ 

for each rotation of the tire, the distance covered by the 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.

$$\begin{gathered} d=84.85\times 10 \\ =848.5 \end{gathered}$$ 

Rounding off to the nearest tenth, we get,

$d=848.5\mathrm{inches}$ 

Thus, the distance covered in 10 rotations by the tire of a 10-speed bicycle is 848.5 inches.