A cuboid whose sides are 8 cm, 27 cm and 64 cm is melted to form a new cube. What is the respective ratio of the total surface area of the cuboid and cube?
Answer & explanation
Correct answer: option 1
The volume of the new cube = Volume of cuboid
⇒ 8 x 27 x 64 = (side)³
⇒ side = \(\sqrt[3]{8 \times 27 \times 64 }\)
= 2 x 3 x 4 = 24
Surface area of cuboid = 2(lb + bh + lh)
= 2(8x27 + 27x64 + 64x8)
= 2 x(216 + 1728 + 512)
= 4912 cm²
Surface area of cube = 6(side)²
= 6 x 24 x24 = 3456 cm²
Ratio = 4912 : 3456 = 307 : 216