# Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m. - Mathematics

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Sum

Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 176 m.

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#### Solution

Let the number of revolutions made by a circular wheel be n and the radius of circular wheel be r.

Given that, area of circular wheel = 1.54 m2

⇒ pir^2 = 1.54   .....[∵ Area of circular πr2]

⇒ r^2 = 1.54/22 xx 7

⇒ r^2 = 0.49

∴ r = 0.7 m

So, the radius of the wheel is 0.7 m

Distance travelled by a circular wheel in one revolution = Circumference of circular wheel

= 2 pir

= 2 xx 22/7 xx 0.7

= 22/5

= 4.4 m ......[∵ Circumference of a circle = 2πr]

Since, distance travelled by a circular wheel = 176 m

∴ Number of revolutions = "Total distance"/"Distance in one revolution"

= 176/4.4

= 40

Hence, the required number of revolutions made by a circular wheel is 40.

Concept: Areas of Sector and Segment of a Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.4 | Q 18 | Page 135
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