Question

If each edge of a cube is increased by $50\%$ then percentage increase in its surface area is

(a) $50\%$ (b) $75\%$ (c) $100\%$ (d) $125\%$

Answer 1

Let a be the edge of the cube.
Then the surface area is 6a^2=S (say)
Now, increased edge = a+(50/100)*a = (150/100)*a = (3/2)a
Then, new surface area=6(3/2*a)^2 =6×(9/4)a^2 =(9/4)S
Increase in surface area =9/4S - S = 5/4S

∴ Percentage increase in surface area =(5/4S)/S*100
= 5/4×100
125%