*Elizabeth Foster*Show bio

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

Lesson Transcript

Instructor:
*Elizabeth Foster*
Show bio

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

Volume, the amount of space an object takes up, can be calculated using geometric principles applied to real-world situations. Understand the application of geometry on volume through a pair of practice problems.
Updated: 11/15/2021

In this lesson, we'll be talking about how you can use volume to solve problems in the real world. But first, we'll warm up with a very brief review of some volume formulas. In a 3-dimensional shape, **volume** describes the amount of space that the shape encloses. In other words, how big is the space inside the shape?

The volume of a cube is equal to the length of one side to the 3rd power. So for example, if you had a cubical box with edges 2 feet long, the volume would be 8 cubic feet.

The volume of a rectangular prism is equal to the length times the width times the height. Let's say your box isn't perfectly square. It's 2 feet long, 3 feet wide, and 4 feet high. In that case, the volume would be 2 * 3 * 4, or 24 cubic feet.

The volume of a cylinder is the area of the base times the height. An example of this is a soup can. If the radius of the soup can is 2 inches and the height is 4 inches, then the volume of the can is pi x 2^2 * 4, or roughly 50.24 cubic inches.

The same goes for a 3-D shape where one side is a triangle, like those boxes you get if you buy just one slice of pizza. Just take the area of the triangle base times the height.

If you're still fuzzy on those, you might want to review them in other lessons before you move on with this one because now we're going to see how we can apply them in real life.

First off, let's fill up a backyard pool.

*Anastasia pays 50 cents per cubic foot of water. She wants to fill her pool, which looks like this. The pool is 15 feet wide by 30 feet long. It's shaped like a rectangle, with a depth changing from 3 feet at the shallow end to 10 feet at the deep end, as shown in the picture. How much will Anastasia pay to fill the pool?*

You can see from the diagram that the pool is 3 feet deep for 5 of its length, and then steadily slopes downward to a depth of 10 feet over the next 25 feet of its length. We can break this pool up into two different shapes: there's a rectangular prism, above the dotted line, and then a triangular prism, below the dotted line. To take our example, it's basically a rectangular box on top of a pizza-slice box. To find the volume of the whole pool, we'll find the rectangular prism and then add it to the triangular prism.

We'll start with the rectangle. This rectangle is 3 feet deep, 15 feet wide, and 30 feet long. So its volume is 3 * 15 * 30, or 1,350 cubic feet.

Now we'll find the volume of the triangular prism. To do this, we'll take the area of the triangular base and multiply it by the distance between each base. In this case, the base is 7 * 25 / 2 feet squared, or 87.5 square feet. Multiply that by 15 to find the total volume of the prism: 1,312.5 cubic feet.

Now we add 1,350 + 1,312.5 to get 2,662.5 cubic feet for the volume of the entire pool. Anastasia pays 50 cents per cubic foot of water, so we'll have to multiply that by 0.50 to get the total price she pays: $1,331.25.

Now you have your pool filled, but if you want a pool party, you need some drinks! So let's head right into the second problem.

Anastasia has a lot of friends, so for Anastasia's pool party, Classic Catering has to deliver 500 gallons of soda, which is equivalent to 115,500 cubic inches of soda. The soda is all in cans with a height of 4 inches and a diameter of 4 inches. The soda company is delivering the cans in dollies with a packable area of 1 foot wide by 1 foot long by 3 feet high. How many dollies does Classic Catering need to deliver all the soda?

This sounds complicated, but let's break it down and take it one step at a time. First we'll figure out how many cans we're actually talking about.

Each can has a diameter of 4 inches and a height of 4 inches. Using this information, we can figure out the volume of each can. The volume of a cylinder is the area of the base times the height. Since the diameter is 4 inches, each can has a radius of 2 inches. The volume of each can is pi*2^2*4. That gives us 16*pi. Rounding this result down to the nearest whole number, that gives us approximately 50 cubic inches for the volume of each can.

We know we have to fit in 115,500 cubic inches of soda in total, so we'll need 115,500/50, or 2,310 cans to hold it all.

Now we know how many cans we have, and we need to find out how many dollies will be necessary to carry them all.

We'll start by figuring out how many cans fit in one dolly. Each can has a diameter of 4 inches, so if you made a line of cans all along the length of a 1-foot dolly, you could fit 3 cans in. That means you could fit 9 cans onto the bottom of the dolly in total. The dolly is 3 feet, or 36 inches tall, and the cans are 4 inches tall. That means we can fit 9 layers of cans into each dolly.

9 cans per layer times 9 layers of cans equals 81 cans per dolly. Since we need to deliver 2,310 cans in total, we'll need a huge parade of dollies. Technically, dividing 2,310 by 81 we'll have about 28.52 dollies, which means that in real life, we'll have 29 dollies: 28 that are completely filled plus 1 that's about half filled.

In this lesson, you learned that **volume** describes the amount of space that the shape encloses. We solved two real-world volume problems using volume formulas.

The volume of a cube is equal to the length of one side to the 3rd power.

The volume of a rectangular prism is equal to the length times the width times the height. Let's say your box isn't perfectly square. It's 2 feet long, 3 feet wide, and 4 feet high. In that case, the volume would be 2 * 3 * 4, or 24 cubic feet.

The volume of a cylinder is the area of the base times the height.

The volume of a 3-D shape where one side is a triangle, like those boxes you get if you buy just one slice of pizza, is the area of the triangle base times the height.

The basic concept for solving all real-world geometry problems is the same: break hard problems down into manageable pieces. You don't have to do everything in one step. Look at the problem conceptually and solve it step by step.

Volume refers to the amount of space that is contained within a particular shape.

Subsequent to studying this lesson, apply your understanding of volume and demonstrate the process of finding the volume of a given shape.

To unlock this lesson you must be a Study.com Member.

Create your account

Volume: Real-World Geometry Problems Quiz

Instructions: Choose an answer and click 'Next'. You will receive your score and answers at the end.

1/5 completed

Create Your Account To Take This Quiz

Try it now
Are you a student or a teacher?

Already a member? Log In

BackRelated Study Materials

Browse by subject