Question

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. 8,650
2. 11,760
3. 13,620
4. 27,440

Answer 1

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