Multiple choice

The cost of etching a glass with design varies directly as the square of its area. It will cost Rs. 16,200 to etch a glass plate of 1 m * 1 m dimensions. What would be the loss to an artist if he were to etch 6 pieces of dimensions 1/3 m * 1/3 m, instead of the 1 m * 1 m piece?

  1. 15,000

  2. 12,000

  3. 17,000

  4. 16,200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cost C = k * A^2. For 1m*1m, A=1, C=16200, so k=16200. For 6 pieces of (1/3)m*(1/3)m, area of one piece is 1/9. Cost per piece = 16200 * (1/9)^2 = 16200 / 81 = 200. Total cost for 6 pieces = 6 * 200 = 1200. Loss = 16200 - 1200 = 15000.

AI explanation

Since the cost varies directly as the square of the area, the cost for one small piece scales by the square of its area relative to the original piece. The area of one small piece is (1/3) * (1/3) = 1/9 square metres, so the cost for one piece is 16200 * (1/9)^2 = Rs. 200. For 6 pieces the total earning is 6 * 200 = Rs. 1200, meaning the loss compared to the original Rs. 16,200 piece is 16200 minus 1200, which equals Rs. 15,000.

Keep practicing — related questions