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In covering a distance s metres, a circular wheel of radius r metres makes s/2πr revolutions. Is this statement true? Why

Solution:

We know that

Distance travelled by a circular wheel of radius r m in one revolution = circumference of the circle = 2πr

Number of revolutions completed in 2πr m distance = 1

Number of revolutions completed in 1 m distance = (1/2πr)

Number of revolutions completed in s m distance = (1/2πr) × s = s/2πr

Therefore, the statement is true.

✦ Try This: A car travels 1 kilometer distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.

It is given that

Total distance covered = 1 km = 100000 cm

We know that

Distance covered by circular wheel in 1 revolution = circumference of circle

Circumference of circle = 2πr

Total number of revolution = 450

2πr × 450 = 100000

So we get

r = (100000 × 7)/(450 × 2 × 22)

r = 35.35 cm

Therefore, the radius of its wheels is 35.35 cm.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 6

Summary:

The statement “In covering a distance s metres, a circular wheel of radius r metres makes s/2πr revolutions” is true

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