Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

Answer

`125%`

Explanation

Consider a cube having edge = a cm
Then, its surface area `= (6a^(2)) cm^(2)`
Now edge = (150% of a) cm `= ((150a)/(100)) cm = (3a)/(2) cm`
New surface area `= {6 xx ((3a)/(2))^(2)} cm^(2) = (27a^(2))/(2) cm^(2)`
Surface area increased `= ((27a^(2))/(2) - 6a^(2)) cm^(2) = ((15a^(2))/(2)) cm^(2)`
Percentage increase in surface area `= ((15a^(2))/(2) xx (1)/(6a^(2)) xx 100)% = 125%`