Chapter 6: Q. 99 (page 366)

The diameter of each wheel of a bicycle is $26$ inches. If you are traveling at a speed of $35$ miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?

Short Answer

Expert verified

The wheels are turning in $453$ rotations per minute.

Step by step solution

Step 1. Given information

The diameter of the cycle is given as $d = 26$ inches and the the speed of travelling is $35$ miles per hour.

Step 2. Required Formula

$1$ mile = $63360$ inches.
Radius of a circle $r = \frac{d}{2}$ , where $d$ is the diameter of the circle.
The perimeter of the circle with radius $r$ is $2 π r$ units.

Step 3. Calculation

As the wheel of the cycle is circular, the path covered by one rotation of the wheel is the perimeter of the circle.

One rotation means $2 π r = 2 π \frac{d}{2} = 2 π \cdot \frac{26}{2} = 26 π$ inches.

Speed of the cycle is $35 \times 63360$ inches per hour.

Therefore, localid="1647258317793" $\frac{35 \times 63360}{60} = 36, 960$ inches per minute.

Now, $26 π$ inches are covered in 1 minute.

Therefore, $36, 960$ inches are covered in $\frac{36, 960}{26 π} = \frac{36, 960 \times 7}{26 \times 22} \approx 452.3$

Therefore, $453$ rotations are done in a minute.

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The diameter of each wheel of a bicycle is $26$ inches. If you are traveling at a speed of $35$ miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Required Formula

Step 3. Calculation

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The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 35 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Required Formula

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Geometry

Decision Maths

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

The diameter of each wheel of a bicycle is $26$ inches. If you are traveling at a speed of $35$ miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?