Bihar Police Constable Model Paper 4

Given:
Each edge of the cube is increased by 50%
Concept Used:
Concept of percentage, It is calculated on the base of 100
For Example, x% means x out of 100
All edges of a cube are equal and the area of one surface is ${\left(\mathrm{length}\mathrm{of}\mathrm{edge}\right)}^2$
Calculation:
Let, the edge of the cube is a unit
Area of one surface is ${\mathit{a}}^2$ square unit
Edge is increased by 50%
⇒ Edge is increased by (50/100) × a
⇒ a/2
The new length of the edge is (a + a/2)
⇒ 3a/2
The new area of one surface is ${\left(3\frac{\mathit{a}}{2}\right)}^2$
⇒ $9\frac{{\mathit{a}}^2}{4}$
Increased on the surface area is $\left(9\frac{{\mathit{a}}^2}{4}\mathit{–}{\mathit{a}}^2\right)$
⇒ $5\frac{{\mathit{a}}^2}{4}$
Percentage increase in the surface area is $\left\{\frac{\left(5\frac{{\mathit{a}}^2}{4}\right)}{\left({\mathit{a}}^2\right)}\right\}$ × 100%
⇒ 125%
∴ The percentage increase in its one surface area is 125%