Filling Volume with Liquid that has specific volume per pound

Question

If I have a liquid that has a specific volume of 26.9 inches cubed per pound, and that liquid sells in the form of a gallon weighing 15.2 lbs, it would be correct to say it's total volume is 15.2*26.9, correct? So that would be 408.88 inches cubed. So if I had a volume of 1.157 inches cubed to fill with that liquid, I would be able to fill that volume 408.88/1.157 = 353.4 times. 353.4 times I would be able to fill that volume if I had that specific liquid; am I correct? Thank you in advance for any assistance.

Answer 1

Yes, if a liquid has a volume of 26.9 cubic inches per pound ($26.9 \frac{in^3}{lb}$) then 15.2 pounds would have a volume of $(26.9 \frac{in^3}{lb})(15.2 lb)= 408.88 in^3$ (I would say "cubic inches" rather than "inches cubed"- but either is correct).

Yes, You could fill that 1.157 cubic inches with this liquid $\frac{408.88 in^3}{1.157 in^3}= 353.4$ times.

Answer 2

It's not clear to me what you are asking.

I think you want to know how many times you can fill a $1.157 \text{ inch}^3$ container if you have $1$ gallon of this liquid.

The best way to solve these problems is to write the units as part of the equation and manipulate them along with the numbers rather than just thinking "do I multiply or divide?". You are given that for this liquid the weight and volume satisfy $$ \frac{26.9 \text{ inch}^3}{1 \text{ pound}} $$ That's an unusual way to discuss the density. It would be more common to write this information as $$ \frac{1 \text{ pound}}{26.9 \text{ inch}^3} =\frac{1}{26.9} \frac{\text{pounds}}{ \text{inch}^3} = 0.0372 \frac{\text{pounds}}{ \text{inch}^3}. $$

According to Google, $1$ gallon is $231$ cubic inches, so a gallon would weigh $$ 0.0372 \frac{\text{pounds}}{ \text{inch}^3} \times \frac{231 \text{ in}^3}{\text{gallon}} = 8.59 \frac{\text{pounds}}{ \text{gallon}} $$

That figure does not match the $15.2$ pounds per gallon in the problem. So I am confused and can't help more until the question is clearer.