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A solid metallic cube of side 9 cm and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted to from a single cube. How much (in Rs.) is the cost to polish the new cube at a rate of Rs. 10 per cm2?1. 8,6502. 11,7603. 13,6204. 27,440 |
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Answer» Correct Answer - Option 2 : 11,760 Given: Dimensions of a solid metallic cube = 9 cm Dimensions of a solid metallic cuboid = 5 cm, 13 cm, 31 cm Rate of Polishing a new cube = Rs. 10 per cm2 Formula Used: Total Surface area of a cube = 6(side)2 Volume of cube = (side)3 Volume of cuboid = (length × breadth × height) Amount to polish the cube = Rate × Total surface area of cube Calculation: Volume of the new cube = Volume of solid metallic cube + Volume of solid metallic cuboid Volume of solid metallic cube = (9 cm)3 = 729 cm3 Volume of solid metallic cuboid = (5 cm × 13 cm × 31 cm) = 2015 cm3 ⇒ Volume of the new cube = (729 cm3 + 2015 cm3) = 2744 cm3 ⇒ (side)3 = 2744 cm3 ⇒ side of new cube = 14 cm Total surface area of the new cube = 6(14 cm)2 = 6 × 196 cm2 = 1176 cm2 Amount to polish the cube = Rs. 10 per cm2 × 1176 cm2 = Rs. 11,760 ∴ Cost to polish the new cube is Rs. 11,760 |
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