Each edge of a cube is increased by 50%.

Question:

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

Solution:

Let 'a' be the edge of the cube

Therefore the surface area of the cube $=6 a^{2}$

i.e., $\mathrm{s}_{1}=6 \mathrm{a}^{2}$

We get a new edge after increasing the edge by 50%

The new edge = a + 50/100∗a

= 3/2∗a

Considering the new edge, the new surface area is $=6 *(3 / 2 a)^{2}$

i.e., $\mathrm{S}_{2}=6 * \frac{9}{4} \mathrm{a}^{2}$

$\mathrm{S}_{2}=\frac{27}{2} \mathrm{a}^{2}$

Therefore, increase in the Surface Area

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

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

So, increase in the surface area

$=\frac{\frac{15}{2} a^{2}}{6 a^{2}} * 100$

= 15/12∗100

= 125%