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The diagram shows a cuboid.The width of the cuboid is 25 cm.The end face of the cuboid is a square.The volume of the cuboid is 1.25 m'.a Work out the length of the cuboid.b Work out the surface area of the cuboid. |
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Answer» Length (1) = 25 cm, Breadth (b) = 20 cm, Height (h) = 5 cm ∵ The box is like a cuboid and total SURFACE area of a cuboid = 2(LB + bh + hl) Area of a box = 2([25 × 20) + (20 × 5) + (5 × 25)] cm2 = 2[500 + 100 + 125] cm2 = 2[725] cm2 = 1450 cm2 Total surface area of 250 boxes = 250 × 1450 cm2 = 362500 cm2 For smaller box: l = 15 cm, b = 12 cm, h = 5 cm Total surface area of a box = 2[lb + bh + hl] = 2[(15 × 12) + (12 × 5) + (5 × 15)] cm2 = 2[180 + 60 + 75] cm2 = 2[315] cm2 = 630 cm2 ⇒ Total surface area of 250 boxes = 250 × 630 cm2 = 157500 cm2 Now, total surface area of both kinds of boxes = 362500 cm2 + 157500 cm2 = 5,20,000 cm2 Area for overlaps = 5% of [ total surface area] ∴ Total area of the cardboard required = [Total area of 250 boxes] + [5% of total surface area] = 520000 cm2 + 26000 cm2 = 546000 cm2 Cost of cardboard: ∵ Cost of 1000 cm2 = Rs. 4 |
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