Question

Each edge of a cube in increased by 50% .Find the percentage increased in numbers area of cube.

Answer 1

As we know that area of cube is given as-

$A=6\times {\left(\text{side}\right)}^2$

Let $a$ be the edge of cube.

Therefore,

Area of cube $=6a^2$

As the each edge of cube is increased by $50\%$.

$\Rightarrow a=a+\frac{50}{100}\times a=\frac{3}{2}a$

Now,

New area of cube $=6\times {\left(\frac{3}{2}a\right)}^2=6\times \frac{9}{4}{a}^2=\frac{27}{2}{a}^2$

Therefore,

Increase in area $=\frac{27}{2}{a}^2-6a^2=\frac{15}{2}{a}^2$

Thus,

Increase $\%=\frac{\left(\frac{15}{2}\right)a^2}{6a^2}\times 100$

$\Rightarrow$ Increase $\%=125\%$

Thus the area is increased by $125\%$.

Hence the correct answer is $125\%$.