Question

42. The diameter of a wheel is 40 cm. How many revolutions will it make on covering 176 m​

Answer 1

The number of revolutions a wheel of diameter 40 cm makes in travelling a distance of 176 m is ( pi = 22/7 )

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Answer 2

Answer:

Given,

Diameter of a wheel = 40

Let,

Number of Revolutions covered by wheel be 'n'

Distance covered by Wheel in 'n' Revolutions = 176m. i.e circumference covered by wheel in 'n' Revolutions.

To Find :-

Number of Revolutions.

Formula Required :-

Circumference of the Circle = 2πr.

Diameter of the Circle = 2 $\sf\times$ r

1m = 100cm

Solution :-

As the Wheel is in Circle Shape we can use the Formula of Circle.

Given, Diameter (d) = 40cm

Diameter = 2r

Radius(r) = $\sf\dfrac{Diameter}{2}$

r = $\sf\dfrac{40cm}{2}$

r = 20cm

$\sf\therefore$ Radius of the Circle = 20cm.

Circumference of the Circle in 'n' Revolutions = 176m

As 1m = 100cm

176m = 176 * 100cm = 17600cm

$\sf\therefore$ Circumference of the Circle in 'n' Revolutions = 17600cm.

Circumference on the Circle in 'n' Revolutions = n *2πr

π = $\sf\dfrac{22}{7}$

Substituting Values :-

17600cm = n* 2 * $\sf\dfrac{22}{7}$ * 20cm

17600cm = n*$\sf\dfrac{880}{7}$

n = $\sf\dfrac{17600cm*7}{880}$

n = $\sf\dfrac{123200}{880}$

n = 140

$\sf\therefore$ Number of Revolutions Covered ny Wheel = 140