# 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**

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

**Summary:**

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

**☛ Related Questions:**

- The numerical value of the area of a circle is greater than the numerical value of its circumference . . . .
- If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2 r . . . .
- The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is . . . .

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