Question

if each edge of a cube is increased by 25%, then find the percentage increased in its surface area

Answer 1

Hlw mate

To find the % increase in surface area, consider:
 
A cube has 6 square surfaces.  The surface area of each surface is the edge length [S] squared (remember L*W?).

So, the surface area of a cube is 6*S^2 = 6*S*S.

If the length of each edge is increased by 25%, the new surface area is  6*(1.25*S)*(1.25*S) 

        Or,   6*( (5/4)*S )*( (5/4)*S ) = 6* (25/16) * S^2

                       = (75/8) * S^2      this is a surface area of   9.375 * S^2 

                            And as a ratio, the increase is  
                                ( 9.375*S*S )  / ( 6*S*S)     =  1.5625 times as large

                            As a %, the surface area would increase by 56.25%.


Hope it helpful