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

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 Click here to see ALL problems on Volume Question 142462: How are surface area and volume affected when the dimension of a box is quadrupled.Answer by ptaylor(2052)   (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