An aluminum sheet 25 cm long, 20 cm broad and 2 cm thick is melted into a cube. The difference in the surface area of the two solids would be
Solution
✅ Correct Option: 4
Melting changes the shape but not the volume. Using the formula for the volume of a cuboid, $l\times b\times h$: $\text{Volume of sheet}=25\times20\times2=1000\text{ cm}^3$ The cube has the same volume, so using $a^3=1000$: $a=\sqrt[3]{1000}=10$ cm | Solid | Surface area formula | Value | |---|---|---| | Sheet ($25\times20\times2$) | $2(lb+bh+hl)$ | $2(500+40+50)=1180\text{ cm}^2$ | | Cube (edge 10 cm) | $6a^2$ | $6\times10^2=600\text{ cm}^2$ | $\text{Difference}=1180-600=580\text{ cm}^2$