Bihar Police Constable Model Paper 7

Given:
The side of a cube is increased by 50%
Concept used:
The total surface area of a cube with side 'a' = 6 × ${\mathit{a}}^2$
Calculation:
The total surface area of a cube with side 'a', = $6{\mathit{a}}^2$
⇒ S = 6 × ${\mathit{a}}^2$
New length of the side = a × 150% = 3a/2
The total surface area of the new cube with side '3a/2',
⇒ ${\mathit{S}}_{\mathit{N}}$ = 6 × ${\left(3\frac{\mathit{a}}{2}\right)}^2$
⇒ ${\mathit{S}}_{\mathit{N}}$ = 6 × ${\mathit{a}}^2\times {\left(\frac{3}{2}\right)}^2$
⇒ ${\mathit{S}}_{\mathit{N}}$ = S × 9/4
⇒ $\frac{{\mathit{S}}_{\mathit{N}}}{\mathit{S}}$ = 9/4
Increase in total surface area = $\frac{\left({\mathit{S}}_{\mathit{N}}-\mathit{S}\right)}{\mathit{S}}$ × 100
⇒ (9 - 4)/4 × 100
⇒ 125%
∴ The total surface area increased by 125%.