Question

In a special racing event, the person who enclosed the maximum area would be the winner and would get Rs 100 for every square metre 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=3m, BC = 10m, CD = BE = 2m

• A. Rs 2914
• B. Rs 2457
• C. Rs 2614
• D. Rs 2500

Answer 1

The Correct Option is B

Total area of figure = ar(semi circle) + ar(rectangle BCDE) + ar(triangle ABE)
\(\frac{\pi}{2}(r)^{2}+(BC\times CD)+( \frac{1}{2} \times AB× BE)\)
\(1.57×(1)^2 + 2 (10×2)+(\frac{1}{2}\times  3×2) \)
\(1.57+20+3=24.57 m^2\)
Therefore, Total amount won \(100 \times 24.57=Rs. 2457\)
The correct answer is (B) :2457