How to Find the Volume of Cones and Pyramids

How to Find the Volume of Cones and Pyramids

In this article, you will learn how to find Volumes of Cones and Pyramids in a few simple steps.

Related Topics

Step by step guide to Find Volume of Cones and Pyramids

A cone is a three-dimensional geometric figure that has a flat surface and a curved surface pointed towards the top point called the vertex.  In other words, the geometric shape of the cone is limited to its base plate and consists of joining straight lines that connect the top of the cone to the points around the base.

To get the volume of the cone, we have to calculate the area of the base surface (circle) and multiply it by the height. Then divide the resulting value by \(3\) to get the volume of the cone. Therefore, the formula for calculating the volume of a cone is as follows:

Volume of Cones: \(\frac{1}{3}\)\(\times\)area of base\(\times\)height

This relation based on mathematical symbols will be as follows:

\(V=\frac{1}{3}\times B\times h=\frac{1}{3}πr^2h\)

Note that in the above relation, \(V\) is the symbol of volume, \(r\) and \(h\) represent the radius of the cone and its height.

A pyramid is a three-dimensional geometric figure that has a polygon base and triangular faces pointed towards the top point called the vertex. The height of a pyramid is a line that is from the top of the pyramid to its base and is perpendicular to the surface of the base.

To calculate the volume of a pyramid, we must first find the area of the base surface and then multiply by its height. Divide the resulting value by 3 and finally, the volume of the pyramid is obtained. Therefore, the formula for calculating the volume of the pyramid will be as follows:

Volume of a pyramid: \(\frac{1}{3}\)\(\times\)area of base\(\times\)height

The above formula is based on mathematical symbols as follows:

\(V=\frac{1}{3}\times B\times h\)

Note that the above formula \(V\) symbolizes the volume of the pyramid, \(b\) is the area of the base surface and \(h\) is the height of the pyramid.

Finding Volume of Cones and Pyramids Example 1:

Find the volume of the following cone. \((π=3.14)\)

Solution:

Use the formula for the volume of cones:\(\frac{1}{3}πr^2h\)

Substitute  for  and  for : \(\frac{1}{3}π(6)^2(15)=565.2 {cm}^3\)

Finding Volume of Cones and Pyramids Example 2:

Find the volume of the pyramid.

Solution:

The volume of a pyramid\(=\frac{1}{3}\times B\times h\)  

\(B=10\times 5=50\)  

Substitute \(50\) for \(B\) and \(12\) for \(h\):

\(=\frac{1}{3}\times B\times h=\frac{1}{3}\times 50\times 12=200 {in}^3\)

Finding Volume of Cones and Pyramids Example 3:

Find the volume of the following cone. \((π=3.14)\)

Solution:

Use the formula for the volume of cones:\(\frac{1}{3}πr^2h\)

Substitute  for  and  for : \(\frac{1}{3}π(5)^2(20)=523.33 {cm}^3\)

Finding Volume of Cones and Pyramids Example 4:

Find the volume of the pyramid.

Solution:

The volume of a pyramid\(=\frac{1}{3}\times B\times h\)  

\(B=6\times 11=66\)  

Substitute \(66\) for \(B\) and \(11\) for \(h\):

\(=\frac{1}{3}\times B\times h=\frac{1}{3}\times 66\times 11=242 {cm}^3\)

Exercises for Finding Volume of Cones and Pyramids

Find the volume of each figure.\((π=3.14)\)

2.

3.

4.

  1. \(\color{blue}{V≈1,272 {cm}^3}\)
  2. \(\color{blue}{V=276 {in}^3}\)
  3. \(\color{blue}{V≈3,014 {cm}^3}\)
  4. \(\color{blue}{V=585 {cm}^3}\)

Related to "How to Find the Volume of Cones and Pyramids"

7 Best Headphones for Online Lessons
7 Best Headphones for Online Lessons
Top 20 Math Websites for Virtual Learning
Top 20 Math Websites for Virtual Learning
Math Skills You Need for the GED Math Test
Math Skills You Need for the GED Math Test
Top Ten Cameras for Classroom Recording
Top Ten Cameras for Classroom Recording
Top 6 Travel-Friendly Teaching Supplies for your Portable Classroom
Top 6 Travel-Friendly Teaching Supplies for your Portable Classroom
List Of the Best Middle School Math Supply for Learning
List Of the Best Middle School Math Supply for Learning
Top Math Websites for Virtual Learning
Top Math Websites for Virtual Learning
Best Blue Light Glasses for Teachers and Students
Best Blue Light Glasses for Teachers and Students
What Skills Do I Need for the ASVAB Math Subtests?
What Skills Do I Need for the ASVAB Math Subtests?
What Skills Do I Need for the SAT Math Test?
What Skills Do I Need for the SAT Math Test?

Leave a Reply

36% OFF

Download Instantly

X

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…