If each edge of a cube is increased by $50$ %, find the percentage increase surface area.

Given: Each edge of a cube is increased by $50$ %

To do: To find the percentage increased surface area of the cube.

Let the side of the cube is $a$.

Surface area of cube$=6a^2$

On $50$ % increase, New side$=\frac{3}{2}a$

New surface area$=6( \frac{3}{2}a)^2$

$=6\times \frac{9}{4}a^2$

$=\frac{27}{2}a^2$

Increased surface area$=\frac{27}{2}a^2-6a^2$

$=\frac{27-12}{2}a^2$

$=\frac{15}{2}a^2$

Percentage increase area$=\frac{Increased\ surface\ area}{original\ surface\ area}\times 100$

$=\frac{\frac{15}{2}a^2}{6a^2}\times100$

$=\frac{15}{2\times 6}\times100$

$=1.25\times 100$

$=125$ %