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A solid cube has a square hole cut through horizontally and a circular hole cut through vertically. Both the holes are cut centrally in appropriate faces. The dimensions of the cube and the hole are shown in the diagram. Calculate the volume remaining after the holes have been cut. (Take π = 3.14)(a) 4995.2 cm3 (b) 5497.6 cm3 (c) 5748.8 cm3 (d) 5994.2 cm3 |
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Answer» Answer: (b) 5497.6 cm3 Remaining volume = (Volume of cube) – (Volume of cuboid formed by cutting the square hole) – (Volume of the cylinder formed by cutting the circular hole) + (Common volume of cuboid and cylinder) = (20)3 – (10)2 × 20 – π × (4)2 × 20 + π × (4)2 × 10 = 8000 – 2000 – 160π = 6000 – 160 π = 5497.6 cm3. Note: The common portion is a cylinder of diameter 8 cm and height 10 cm (side of square). |
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