Question

Each side of a cube is increased by $50$%. Then the surface area of the cube increases by ?

• A. $50$%
• B. $100$%
• C. $125$%
• D. $150$%

Answer 1

The correct option is C $125$%

Total surface area of a cube of edge a $=6a^2$
If the edge is increased by $50$, then new side $A=\frac{150}{100}a=\frac{3}{2}a$
Increase in surface area $=$ New surface area - Old Surface area $=6A^2-6a^2=6\times {\frac{3}{2}a}^2-6a^2=6a^2(\frac{9}{4}-1)=\frac{5}{4}\times 6a^2$

increase in the total surface area $=\frac{\frac{5}{4}\times 6a^2}{6a^2}\times 100=125$