Q. 434.3( 13 Votes )

An elastic belt i

Answer :

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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