Question

Each edge of a cube is increased by $50\%$. What is the percent of increase in the surface area of the cube?

• A. $50\%$
• B. $125\%$
• C. $150\%$
• D. $300\%$

Answer 1

The correct option is B $125\%$

Let an edge of cube be $2a$

Surface area of cube, S${}_1$$=6\times (2a{)}^2=24a^2$

Given that each edge is increased by $50\%$, i.e. new edge length $=3a$

New surface area of cube, S${}_2=6\times (3a{)}^2=54a^2$

$\%$ increase in the surface area $=(S_2-S_1)\times \frac{100}{S_1}$

$=\frac{30a^2}{24a^2}\times 100$

$=125\%$