Question

A batsman is holding a 1 m long bat in his hand. To make a shot, the batsman swings the bat through an angle of 60 °. His arm length is 75 cms. Considering his hand and the bat acting as a straight line, what will be the area swept by the bat.

• A. 1.387 $m^2$
• B. 1.562 $m^2$
• C. 1.305 $m^2$
• D. 1.854 $m^2$

Answer 1

The correct option is C

1.305 $m^2$

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 = $\frac{\Theta }{{360}^{\circ }}\times \pi R^2$ = $\frac{60}{360}\times \frac{22}{7}\times {1.75}^2$ = 1.6 $m^2$

The radius of the area swept by the hand = 0.75 m

The area swept by the hand = $\frac{\Theta }{{360}^{\circ }}\times \pi r^2$ = $\frac{60}{360}\times \frac{22}{7}\times (0.75{)}^2$ = 0.295 $m^2$

Therefore, The area swept by the bat = area swept by the bat and hand – area swept by the hand = 1.6 - 0.295 = 1.305$m^2$

The area swept by the bat is 1.305$m^2$ .