Q. 304.5( 13 Votes )

# An elastic belt i

On the basis of question the figure can be redrawn as follows:

We know that, tangent of a circle is perpendicular to the radius of the circle through the point of contact

∴∠ OAP = 90o

Now, in right triangle OAP, we have

Also, in right triangle OAP we have:

So, AOB = 60o + 60o

= 120o (i)

Reflex AOB = 360o – 120o

= 240o

We know that, length of the belt which is in contact with the pulley = ADB

= Length of major arc

= 20.93̅ cm

Now, in right-angled triangle OAP we have:

We know that,

We know that,

= 26.17 cm2 (Approx.)

Area of shaded region = Area of triangle OAP + Area of triangle OBP – Area of minor sector OABC

= 25 × 1.73 – 26.17

= 17.08 cm2

Hence, area of the shaded region will be 17.08 cm2

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