A large balloon has a volume of 1.767 cubic feet. It is filled with helium, which has a density of 0.010238 pounds per cubic foot. What is the mass, in pounds and correct to three decimal places, of the helium in the balloon?
So the first thing we need to decide is what type of question is this. Well, if we take a look, we’ve got volume, density, and mass. And what this tells us is that we’re going to use the mass-volume-density triangle. And this enables us to choose the correct formula to work out the mass, volume, or density given the other two. So let’s see what we’re looking for.
First of all, we’ll write down the information we’ve got. So we’re told that the volume of the balloon is 1.767. And that’s cubic feet. We’re told the density of helium is 0.010238 pounds per cubic foot. And we’re not told the mass because this is what we’re looking for.
Well, if the mass is what we’re looking for, we look at the other two, so density and volume. Because they’re next to each other, it means we’re gonna multiply them together. So therefore, the formula we’re going to use is that mass is equal to density multiplied by volume. And it’s always worth checking out the units to make sure that you have the correct formula. So if you’re not sure that you’ve got the correct formula, you can look at units.
So let’s think that the mass is pounds. And it’s gonna be equal to the density. Well, we’re told that the density is pounds per cubic foot. And then, we’ve got this multiplied by the volume. And we’re told that the volume is in cubic feet. Well, if we multiply pounds per cubic feet by cubic feet, then what we’re gonna have is the cubic feet is gonna cancel. And we’re left with pounds. And this is what we want the mass to be in.
Okay, so now let’s substitute our values into the formula. So the mass is gonna be equal to 0.010238 multiplied by 1.767 cause that’s the density multiplied by the volume. So that’s gonna be equal to 0.01809054, etc. So have we finished here? Well no, cause we need to check the accuracy. And the question has asked us to leave it correct to three decimal places.
So therefore, the mass of helium is gonna be equal to 0.018 pounds to three decimal places.
And the way I rounded that was I looked at the third decimal place, which is where the eight is. And then I take a look at the digit or number to the right of it. And this is the deciding number. Well, if this is less than five, then the number remain as it is. If it’s five or greater, then we round it up.
Well, as it’s zero, that means the eight remained as it was. So we said that the answer was 0.018 pounds to three decimal places.