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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