A batsman is holding a 1 m long bat in his hand. To make a shot, the batsman swings the bat by an angle of 60 degrees. His arm length is 75 cms. Considering his hand and the bat is acting as a straight line, what will be the area swept by the bat.
1.305 m2
Here we need to find the area swept by the bat. We can assume that the area swept by the hand is a sector. This way we will be able to conclude that the area swept by the bat as the difference between the area swept by the hand and bat together and the area swept by the hand.
i.e. Area swept by the bat = Area swept by the hand and bat – Area swept by the hand
The radius of the area swept by the hand and the bat = length of the bat + length of the hand = 100 + 75 = 1.75 m
Therefore, The area swept by the bat and hand = Θ360∘×πR2 = 60360×227×1.752 = 1.6 m2
The radius of the area swept by the hand = 0.75 m
The area swept by the hand = Θ360∘×πr2 = 60360×227×(0.75)2 = 0.295 m2
Therefore, The area swept by the bat = area swept by the bat and hand – area swept by the hand = 1.6 - 0.295 = 1.305m2
The area swept by the bat is 1.305m2 .