Study the applications of volume in real life. Get the formula for volume, learn about calculating volume for various shapes and see real world volume examples. Updated: 11/21/2023
Volume in Real Life | Formula, Calculation & Examples
Table of Contents
ShowFrequently Asked Questions
What is volume with example?
Volume is the amount of space an object takes up. It is typically measured using cubic units, and estimated using a variety of formulas. For example, a rectangular bathtub that is 1 foot tall, 2 feet wide, and 4 feet long will have a volume of 8 cubic feet. This can be calculated by multiplying length times width times height.
How is volume shown in the real world?
In mathematics, volume is the amount of three-dimensional space an object takes up. In the real world, volume is often measured using cubic units (i.e. cubic meters) or estimated using various formulas, including length times width times height for rectangular prisms.
What do we use volume for?
In the real world volume calculations are used for many purposes. For example, knowing the shape of a gasoline tank (including length, width, height, or even circumference, depending on the tank's shape) can allow automobile manufacturers to calculate exactly how much gasoline a car's tank will hold.
Table of Contents
ShowThe question "what is volume?" can have a few answers, depending on if one is asking about the knob on a radio or the formula in a geometry textbook. But in mathematics, volume is defined as the amount of three-dimensional space that an object takes up. It is typically measured using cubic units, including cubic meters, cubic feet, or cubic inches. It can also be measured using units like liters, milliliters, or gallons.
Many everyday items that one might buy are sold according to their volume. For example, in the United States, gasoline is sold by the gallon, while in many other countries it is sold by the liter. At the grocery store, milk is often sold by the gallon, while soda and other beverages are sold by the ounce or by the liter. Even soil is often sold according to its volume; loam is often sold by the cubic yard, for example. In all of these cases, it is not the mass or the density of the object that matters. Rather it is the amount of space — the volume — that the object takes up.
Volume in Real Life
There are many examples of the concept of volume in real life. Below is a list of some everyday examples where knowing or estimating volume is of particular importance.
- Buying Mulch: For anyone who might someday buy mulch for their yard, knowing about the concept of volume will be of particular importance. Mulch is typically sold by its volume rather than its weight. Some stores sell bags measured in cubic feet. Some vendors sell truckloads by the cubic yard. When comparing prices, it will be important to know that there are 27 cubic feet inside one cubic yard.
- Cooking: Cooking is a world where mass and volume are sometimes interchangeable. Some recipes ask the chef to add "one cup of flour" while another might ask for ingredients to be added by their weight. It is important to note that volume is typically used to measure liquids (and sometimes solids) using units like cups, ounces, and pints in the English system. However, confusingly there is also a unit of weight that is also called the "ounce."
- Sea-Level Rise: Because of anthropogenic global warming, sea levels in the ocean are rising by the decade. But knowing exactly how much, and how fast, they will rise is an important projection for scientists. By calculating the volume of ice within ice sheets, including the ones in Antarctica and Greenland, scientists are able to forecast sea-level rise. The good news? It is happening slowly, at a rate of about 1 inch per decade as of 2022. The bad news? It is accelerating, and sea levels will probably be 1.5-3 feet higher by the year 2100.
- Boat Building: Volume calculations are essential for engineers responsible for designing and building boats. In order to float, a boat must have a density that is less than that of water. And in order to estimate a boat's density, one must have an idea of the boat's mass and volume (
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In geometry classes across the globe, a student will ask "What is the formula for volume?" only to receive a litany of answers from their teacher. In truth, there are dozens of formulas for calculating volume, all of which attempt to do the same thing: estimate the amount of space a three-dimensional shape takes up. Because volume is measured using cubic units, the formulas for cubes and rectangles are the simplest. Meanwhile, formulas for cylinders, cones, and spheres require a bit more work. Below is a list of some of the basic geometric formulas for volume (V).
- Cube:
- Rectangular Prism:
- Pyramid:
- Cylinder:
- Cone:
- Sphere:
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Real-world volume examples often use formulas, like the ones above, to estimate an object's volume. Although there is no such thing as a perfect sphere or a perfect cube, in real life, simple geometric formulas can provide a remarkably accurate estimate, whether one is calculating the volume of a bathtub, a flower vase, or even a water balloon.
Example #1
A bathtub is one foot tall, two feet wide, and four feet long. Water in the area costs $0.25 per cubic foot. How much money will the bathtub cost to fill?
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Example #2
A cylindrical flower vase is 20 centimeters tall and has a radius of 10 centimeters. How much water will it take to fill a row of eight vases?
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Example #3:
Two different water balloons are held, one in each hand, by a young boy. One balloon has a radius of 3 inches. The other has a radius of 4 inches. How much additional water is contained by the bigger balloon?
That's more than double!
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Volume is defined as the amount of three-dimensional space that an object takes up. It is typically measured using cubic units, including cubic meters, cubic feet, or cubic inches. It can also be measured using units like liters, milliliters, or gallons. Many everyday items that one might buy are sold according to their volume including gasoline, various beverages, and soil or mulch. Volume also has many scientific applications as well, including the forecasting of sea-level rise according to the volume of melting ice, as well as boat-building and the engineering of cargo ships.
There are dozens of formulas for volume. Because volume is measured using cubic units, the formulas for cubes and rectangles are the simplest. Meanwhile, formulas for cylinders, cones, and spheres require a bit more work. The volume of a cube can be calculated using the formula
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Video Transcript
Volume
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.
Problem 1
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?
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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.
Problem 2
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.
Lesson Summary
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 Formulas
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Volume refers to the amount of space that is contained within a particular shape.
Learning Outcomes
Subsequent to studying this lesson, apply your understanding of volume and demonstrate the process of finding the volume of a given shape.
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