Michael H. | Statistics (including research analyses and reports), ACT/SAT, algebraStatistics (including research analyses ...

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Since 2 of 3 dimensions are in inches, there are 2 response choices choice with cubic inches versus 1 with cubic centimeters, 2 of three tray dimensions are in inches, and our gallon conversion factor yields cubic inches, it should be easiest if we start by converting the only metric dimension, the tray depth of 4 cm, to inches. Since there are exactly 2.54 inches per cm, we start by dividing 4 by 2.54.

Here is a trick if you can’t remember whether to divide or multiply by your conversion factor, CF =2.54 cm/in. You started with X cm and want Y inches the answer is either

1) Y in = X cm x (CF in/cm) or 2) Y in = X cm / ( CF in /cm) In the first formula , the cm in the right half of the equation cancel leaving in, which is what you want. In the second formula, you end up with a denominator of squared cm, which is definitely not what you want. Scientists and their students often apply this method called unit analysis to much more complex equations

In our case, 4cm /( 2.54 cm/in) = 1.5748 in. The number of significant figures is determined by the 4 cm, since 2.54 is an absolute constant. I don’t know to what accuracy the 4 cm height was measured, so let’s keep 3 digits for now.

The volume of the tray is just V = L x W x H -- 10 in x 14 in x 1.57 in = 219.8 cubic in.

We are given that 1 gallon equals 231 cubic inches which overflows the tray.

Normally, we could stop here, because there is only one answer where the paint overflows the tray. This kind of reasoning can save you time on standardized tests. However, since we are not working against the clock, let’s subtract the volume of the tray (219.8 cubic in ) from one gallon (231 cubic inches) leaving an overflow of 10.53 cubic inches, which confirms our choice.