Question

Each edge of a cube is increased by $50$. Find the percentage increases in the surface area of the cube.

Answer 1

Let $a$ be original side

Surface area is $6a^2$

Changed one is $a+\frac{50}{100}a=\frac{3}{2}a$

Surface area is $6{\left(\frac{3}{2}a\right)}^2=\frac{27}{2}{a}^2$

The increase percent is $\frac{\frac{27}{2}{a}^2}{6a^2}\times 100\frac{9}{4}\times 100=225\%$