Calculating the volume of objects has many real-world applications. Students use specific formulas to calculate the volume of three dimensional shapes.

Author

Katie Wickliff

Published

November 14, 2023

Author

Katie Wickliff

Published

Nov 14, 2023

Author

Katie Wickliff

Published

Nov 14, 2023

Key takeaways

- Volume refers to the amount of space an object takes up.
- Volume formulas vary by shape.
- When calculating the volume of a circular shape, use “pi,” which is approximately 3.14

Table of contents

Whether you’re measuring the ingredients to bake a cake, adding potting soil to a gardening bed, or simply filling your water bottle before a hike, knowing how to measure volume is an essential part of our daily lives.

In this article, we’ll cover the basics of volume and include the formulas to calculate the volume of common shapes. We’ll also include practice problems for each type of shape, to give your student practice using these formulas. For even more practice, head over to DoodleLearning’s award-winning math app. Let’s get started!

Simply put, volume is the measurement of how much space something takes up. In a three dimensional (3D) object, such as a pyramid or cone, volume is also often referred to as “capacity.” In a two-dimensional object, volume is known as “area.”

Students learn **how to calculate volume **by using equations. These equations vary by shape. When your student is first learning to calculate volume, they’ll start by learning to calculate the **volume formulas** of common 3D shapes, such as these:

To calculate the volume of a cylinder, we need to know the height of the cylinder and the radius of the base. We also need to know the approximate value of “pi,” a measurement used with circular shapes.

Pi= 3.14 which is represented as **π** in formulas.

**Volume= ***πr**2**h*

In this example, the radius “r” is 6 inches, and the height “h” is 11 inches.

V= π (6)²(11)

V= π (36) (11)

V= π 396

V= (3.14) (396)

V= 1,243.44 in³

When working with volume, we always use cubic unit measurement, which is represented by “³”

To find the **volume of a cone**, we need to know the height and the radius of the base. Just like with the volume of a cylinder (shown above) we also need to know the approximate value of “pi”.

To find the **volume of a cone**, we use this formula:

**Volume=*** ⅓ **πr**²**h*

When calculating the volume of a sphere, we need to know the radius. Just like with cylinders and cones, we also need to know the approximate value of Pi.

To find the **volume of a sphere**, we use this formula:

**Volume = 4/3 πr****3**

In the example above, the radius is 4 cm.

Volume = 4/3 π4³

V= 4/3 π64

V= 4/3x 64x*π*

V= 85.33π

** V= 267.94**³

To calculate the volume of a rectangular prism, we need to know three measurements: the length(l), the width(w), and the height(h).

To find the volume of a rectangular prism, we use this formula:

**Volume= length x width x height**

Volume= 1 x 3 x 2

Volume= 6 ft³

**Find the volume of the sphere. Use 3.14 for π.**

**Find the volume of the cone. Use 3.14 for π**

**Find the volume of the rectangular prism.**

**A drawer is 4 feet long, 2 feet wide, and 3 feet high. What is the volume of the drawer? **

Volume= 4/3*π3*³

Volume= 4/3*π27*

V= 4/3 x 3.14 x 27

**V= 113.04mm****³**

V= ⅓ π (2)²(7)

V= ⅓ π (4) (7)

V= ⅓ π 28

V= (⅓)(3.14) (28)

**V= 29.3 cm³**

Volume= 4 x 6 x 3

**V= 72in³**

V= 4x2x3

**V=24ft³**

The definition of volume in math is the amount of space an object takes up.

We measure volume by using formulas that differ based on the shape of the object.

Volume formula differs based on the type of shape. When measuring the volume of a cylinder, use the formula v= πr²h. To find the volume of a cone, use the formula volume= ⅓ πr²h. To find the volume of a rectangular prism, use the formula v= l x w x h. To find the volume of a sphere, use the formula v= 4/3 πr3

Lesson credits

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

Katie Wickliff

Katie holds a master’s degree in Education from the University of Colorado and a bachelor’s degree in both Journalism and English from The University of Iowa. She has over 15 years of education experience as a K-12 classroom teacher and Orton-Gillingham certified tutor. Most importantly, Katie is the mother of two elementary students, ages 8 and 11. She is passionate about math education and firmly believes that the right tools and support will help every student reach their full potential.

Parents, sign up for a DoodleMath subscription and see your child become a math wizard!

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