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Differentiating Between Area & Volume

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will examine the basic differences between area and volume. We will go over examples of each and learn how to solve for each in different scenarios.

Area vs. Volume in your Bedroom

You just bought a new house a need to put some carpet in your bedroom. Your husband tells you to find the volume of the bedroom before he goes to the store so he knows how much carpet to buy. You set out trying to find the volume of the room but realize you actually need the area! How confusing!

Area

To find out how much carpet you need, you actually need to find the area of the floor of your bedroom, not the volume. Area is a two-dimensional measurement of the surface of an object. In our case, we are measuring the surface of the floor of your bedroom. Because it is two-dimensional, we will only use two measurements to find the area.

Let's say your bedroom is in the shape of a rectangle. To find the area of the bedroom, you will simply multiply the measurement of the length of the room by the measurement of the width of the room. If your room is 25 feet long and 18 feet wide, simply multiply 25 feet by 18 feet to get an area of 450 feet squared. This means your husband needs to buy 450 square feet of carpet to cover the floor of your new bedroom.

Area of Bedroom
Area

One thing to note about area is that the units will be squared. This is because you will always be multiplying two measurements together. Just like how x multiplied by x will give you x2, feet multiplied by feet will give you feet2. To ensure you do this correctly, make sure your starting measurements are in the same units!

Volume

Your silly husband initially asked you to find the volume of the bedroom. Volume is a three-dimensional measurement of how much space an object takes up. If we were to measure the volume of your bedroom, we would need three different measurements. We already know the length is 25 feet and the width is 18 feet, but we also need the height. If the height is 20 feet, we can multiply all three measurements together to get a volume of 9,000 feet cubed. This means that your bedroom takes up 9,000 cubed feet! Not useful in terms of carpeting the floor.

Volume of Bedroom
Volume

Note that units for volume will always be cubed. Just as x multiplied by itself three times will give x3, feet multiplied by itself three times will result in feet3.

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