A metal sheet measuring 27 cm in length, 8 cm in width, and 1 cm in thickness is melted and reshaped into a cube. What is the difference between the surface areas of the original sheet and the resulting cube?

Explanation

First, calculate the volume of the metal sheet: 27 cm × 8 cm × 1 cm = 216 cm³. Since the metal is melted and formed into a cube, the cube's volume is also 216 cm³. The edge length of the cube is the cube root of 216, which is 6 cm. Next, find the surface area of the original sheet (a cuboid): 2 × (27×8 + 8×1 + 27×1) = 2 × (216 + 8 + 27) = 2 × 251 = 502 cm². The surface area of the cube is 6 × 6² = 6 × 36 = 216 cm². The difference between the surface areas is 502 cm² - 216 cm² = 286 cm².