Liquid Volume

Area vs. Volume 

Since volume is affected by the size of the dimensions, we always need to calculate the volume to determine if shapes can hold the same amount.

Imagine you have these two containers. Container A is filled with orange juice. Container A doesn’t fit in the refrigerator, so you want to move all the orange juice to Container B, which does fit in the refrigerator. These two containers look different – one is short and wide, and the other is tall and narrow. It might seem like they don’t have the same volume, or can’t hold the same amount of orange juice, but we need to calculate their volumes to be sure.

Container A has the dimensions 5 inches by 2 inches by 4 inches. Container B has the dimensions 2 inches by 2 inches by 10 inches. Let’s find the volume of each container. We write the formula, and now we plug in. Volume = 5 x 2 x 4. 5 x 2 = 10. 10 x 4 = 40. The volume of Container A is 40 cubic inches. Now let’s look at Container B. We substitute in the dimensions, and now we solve. 2 x 2 = 4. 4 x 10 = 40. Container B also has a volume of 40 cubic inches. They have equivalent volumes, so we will be able to pour orange juice from Container A into Container B.

Now imagine we have these two containers. The two containers have a similar shape, but we cannot assume they have the same volume, and we cannot assume that we can pour orange juice from Container A into Container B. Let’s calculate their volumes. Container A is 3 inches by 3 inches by 4 inches, so its volume = 36 cubic inches. Container B is 3 inches by 2 inches by 4 inches, so its volume is 24 inches cubed.

Volume is affected by the size of the dimensions, so shapes that look different can have the same volume, and shapes that look similar can have different volumes.