Question : A solid metallic cube of side 9 cm and a solid metallic cuboid having dimensions 5 cm,13 cm, and 31 cm are melted to form a single cube. How much (in INR) is the cost to polish the new cube at a rate of INR 10 per cm2?
Option 1: 8,650
Option 2: 27,440
Option 3: 13,620
Option 4: 11,760
Correct Answer: 11,760
Solution : Volume of the cube = (side) 3 = 9$^3$ = 729 cm 3 Volume of the cuboid = 5 × 13 × 31 = 2015 cm 3 Volume of the single cube = volume of cube + volume of cuboid = 729 + 2015 = 2744 cm 3 Side of Recast cube ⇒ Side 3 = 2744 ⇒ Side = 14 cm So the total surface area of the cube = 6 × 14 × 14 = 1176 cm 2 Cost of painting at Rs. 10 per cm 2 = 10 × 1176 = Rs. 11760 Hence, the correct answer is 11760.
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Question : A 9 cm solid metallic cube and a solid metallic cuboid having dimensions 5 cm, 13 cm, and 31 cm are melted and recast into a single cube, What is the total surface area (in cm2) of the new cube?
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