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A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm.The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2 , find the total expenses required for polishing and painting the surface of the bookshelf. |
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Answer» Outer length, l = 25 cm. outer breadth, b = 85 cm. outer height, h = 110 cm. Outer surface area = lh + 2lb + 2bh = lh + 2(lb + bh) = 85 × 110 + 2(85 × 25 + 25 × 110) = 9350 + 9750 = 19100 cm2 . Area of front face, = [85 × 110 – 75 × 100 + 2(75 × 5)] = (9350 – 7500 + 2(375)] = 9350 – 7500 + 750 = 11000 – 7500 = 3500 cm2 . Area to be polished, = 19100 + 3500 = 22600 cm2 . Cost of polishing 1 cm3 is Rs. 0.20. Cost of polishing 22600 cm3 … ? … = 22600 × 0.20 = Rs. 4520. Length of horizontal shelf, l = 75 cm. breadth, b = 20 cm. height, h = 30 cm. Area of horizontal shelf = 2(l + h)b + lh = [2(75 + 30) × 20 + 75 × 30] = (4200 + 2250] cm2 . = 6450 cm2 . ∴ Area of painting 3 horizontal rows = 3 × 6450 = 19350 cm2 . Cost of painting for 1 cm3 is Rs. 0.10. ∴ Cost of painting 19350 cm3 … ? = 19350 × 0.10 = Rs. 1935. ∴ Total cost of polish and painting = Rs. 4520 + Rs. 1935 = Rs. 6455. |
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