Arectangular jewelry box costs $125 to gold plate. calculate the cost of gold plating a box which is similar in shape and that holds 8 times as much. the answer is not $1,000 or $8,000 or $64,000

To determine the amount of gold plating necessary for the similar box, you will use the fact that it is 8 times larger in volume to determine how many times larger the area is.  This would be what you will multiply $125 by.

Volume is a three dimensional measurement, so the fact that it is 8 times larger tells us each dimension was 2 times larger (2 x 2 x 2=8).  

Area is a two dimensional measurement, so the area would have been 2 x 2 or 4 times larger.  This means the price would be 4 times as much.
$125 x 4 = $500.

It will cost $500 to gold plate the similar jewelry box.