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Question 134

In a special racing event, the person who enclosed the maximum area would be the winner and would get Rs 100 for every square meter of area covered by him/her. Johnson, who successfully completed the race and was the eventual winner, enclosed the area shown in figure below. What is the prize money won? (Note: The arc from C to D makes a complete semi-circle).

AB = 3 m, BC = 10 m, CD = BE = 2 m

Solution

Total area of figure = ar(semi circle) + ar(rectangle BCDE) + ar(triangle ABE)

= $$\frac{\pi}{2} (r)^2 + (BC\times CD)+(\frac{1}{2}\times AB\times BE)$$

= $$1.57 \times(1)^2 + (10\times 2)+(\frac{1}{2}\times 3\times 2)$$

= $$1.57 + 20+3=24.57$$ $$m^2$$

$$\therefore$$ Total amount won $$100\times24.57=Rs.$$ $$2457$$

=> Ans - (B)

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