The length of each edge of a cube is increased by 25%. By what percentage has the surface area of the cube increased?

Question

The length of each edge of a cube is increased by 25%. By what percentage has the surface area of the cube increased?

Answer 1

 

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%

Answer 2

The volume of a cube is found by multiplying (length)(width)(height) or  V = LWH

 

If we increase each dimension by a factor of 25% or 1/4

Our new dimensions are (5/4)L , (5/4)W, and (5/4)H

 

Finding the new volume gives (5/4 L)(5/4 W)(5/4 H)  = (5/4)³LWH = (125/64) LWH = 1.953125 LWH

 

This an increase by a factor of approximately 95.3%

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As Philip noted the scale factor is 1.25 but it's a cubic volume, not square

1.25³ = 1.953125 which is the same answer as one gets by multiplying it

out as I did above.

Answer 3

A 25% increase in the length of each side equates to a scale factor of 1.25.  The surface area increases as the square of the scale factor, (1.25)² = 1.5625.