SOLUTION: How are surface area and volume affected when the dimension of a box is quadrupled.

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Question 142462: How are surface area and volume affected when the dimension of a box is quadrupled.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Volume(V) of a box=Length(L) times Width(W) times Height(H) or:

V=LWH --------------------------------------------eq1
now if we quadruple the dimensions, we have:
V1=4L*4W*4H=64LWH--------------------------------eq2
Substitute LWH=V from eq1 into eq2:
V1=64V
So, when we quadruple the dimensions, the volume is increased by a factor of 64
Surface Area(SA) of a box equals Area of Top plus Area of Bottom plus Area of Front plus Area of Back plus Area of Each Side
Area of Top plus Bottom=2LW
Area of Front plus Back=2WH
Area of the two Sides=2LH, so:
SA=2LW+2WH+2LH----------------------------------------eq3
now if we quadruple the dimensions, we have:
SA1=2*4L*4W+2*4W*4H+2*4L*4H and this equals
SA1=16(2LW)+16(2WH)+16(2LH) from the right side, factor out 16:
SA1=16(2LW+2WH+2LH)-----------------------------------------eq4
substitute 2LW+2WH+2LH=SA from eq3 into eq4 and we get:
SA1=16SA
So, when we quadruple the dimensions, the surface area is increased by a factor of 16


Hope this helps---ptaylor