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Question Video: Calculating the Distance Travelled by a Bicycle Given the Radius of Its Wheel Mathematics • 11th Grade

A bicycle wheel has a radius of 35 cm. How far to the nearest meter does Emma cycle if the wheel revolves 250 times?

02:27

Video Transcript

A bicycle wheel has a radius of 35 centimeters. How far to the nearest meter does Emma cycle if the wheel revolves 250 times?

We’re told that Emma’s bicycle wheel, which is a circle, has a radius of 35 centimeters. That’s the distance from the center of the wheel out to its edge, or circumference. We’re then told that the wheel revolves 250 times and asked how far Emma will have cycled in that time. Each time Emma’s wheel completes one full revolution, the distance the bicycle travels will be equal to the circumference of the wheel. The total distance traveled will therefore be 250 times the wheel’s circumference.

The circumference of a circle can be calculated using the formula two 𝜋𝑟, where 𝑟 represents the radius of the circle. We’ve been given this value, so we can substitute 𝑟 equals 35 into this formula. That gives two 𝜋 multiplied by 35, which is 70𝜋. We could evaluate this as a decimal. But as we haven’t finished our calculation yet, we’ll keep it as a multiple of 𝜋 for now so that the next stage of our calculation is exact. Then, multiplying this value by 250, we have that the total distance traveled is 250 multiplied by 70𝜋. That’s equal to 17,500𝜋, or as a decimal 54,977.871 continuing.

At this point, we observe that we’re asked to give our answer to the nearest meter. But the measurement for the radius was given in centimeters. We know that one meter is equivalent to 100 centimeters. So we can convert this value to meters by dividing by 100. Finally, we’re asked to give the answer to the nearest meter, so we need to round up. By first calculating the circumference of the wheel, we’ve found that the total distance Emma cycled was 550 meters to the nearest meter.

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