A solid metallic cube of side 9 cm and solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted to form single cube. How much(in ₹) is the cost to polish the new cube at a rate of ₹10 per cm2?
Answer & explanation
Correct answer: option 4
We know that,
Volume of cube = (side)3
Volume of cuboid = length × breadth × height
Total surface area of cube = 6 × side2
We have,
Side of cube = 9 cm
Length of the Cuboid = 5 cm, breadth = 13 cm, height = 31 cm
Volume of Solid metallic cube = (9)3 = 729 cm3
Volume of Solid metallic cuboid = 5 × 13 × 31 = 2015 cm3
Volume of single cube = Volume of Solid metallic cube + Volume of Solid metallic cuboid
= 729 + 2015 = 2744 cm3
Side of Recasted cube = (Side)3 = 2744
= side = 14 cm
Total surface area of cube = 6 × 14 × 14 = 1176 cm2