A pool in the shape of a right rectangular prism holds 360 cubic feet of water. If the length of the pool and the depth of the water in the pool are 10 feet and three feet, respectively, what is the width of the pool?
Here is a right rectangular prism, and there’s a pool in this shape. A pool that holds 360 cubic feet of water has a volume at 360 feet cubed. The volume of a right rectangular prism can be found by multiplying its length times its width times its height. This pool has a length of 10 feet and a depth of three feet. And we’re trying to find its width. Since we know its volume is 360 feet cubed, its length is 10 feet and its depth is three feet. Another way to say that would be a height of three feet.
We can use this information to solve for 𝑤, the width. 10 feet times three feet equals 30 feet squared. 30 foot squared times the width will equal the volume. To find the width, we need to divide both sides of the equation by 30 foot squared. 360 divided by 30 equals 12. And feet cubed divided by feet squared equals feet. The width of this pool is 12 feet.
You can solve this type of problem without a picture. You could say the volume of 360 equals 10 times three times the width, 360 equals 30𝑤, and then divide both sides by 30. And again you’ll get 12 equals 𝑤. But by including the units, you can make sure that each of the values have been given in the correct units. If, for example, one of the values we’re given in inches, you would need to convert it to feet before you did any multiplication or division, as it’s important to keep our units straight. This problem has only asked us for the width of the pool, which we found to be 12 feet.