Finding the Volume of a Cone
Learning Outcomes
- Find the volume of a cone
The first image that many of us have when we hear the word ‘cone’ is an ice cream cone. There are many other applications of cones (but most are not as tasty as ice cream cones). In this section, we will see how to find the volume of a cone. In geometry, a cone is a solid figure with one circular base and a vertex. The height of a cone is the distance between its base and the vertex.The cones that we will look at in this section will always have the height perpendicular to the base. See the image below.
The height of a cone is the distance between its base and the vertex.



Volume of a Cone
For a cone with radius and height .
example
Find the volume of a cone with height inches and radius of its base inches. SolutionStep 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
Step 2. Identify what you are looking for. | the volume of the cone |
Step 3. Name. Choose a variable to represent it. | let = volume |
Step 4. Translate. Write the appropriate formula. Substitute. (Use for ) | |
Step 5. Solve. | |
Step 6. Check: We leave it to you to check your calculations. | |
Step 7. Answer the question. | The volume is approximately cubic inches. |
try it
[ohm_question]146818[/ohm_question]example
Marty’s favorite gastro pub serves french fries in a paper wrap shaped like a cone. What is the volume of a conic wrap that is inches tall and inches in diameter? Round the answer to the nearest hundredth.Answer: Solution
Step 1. Read the problem. Draw the figure and label it with the given information. Notice here that the base is the circle at the top of the cone. | ![]() |
Step 2. Identify what you are looking for. | the volume of the cone |
Step 3. Name. Choose a variable to represent it. | let V = volume |
Step 4. Translate. Write the appropriate formula. Substitute. (Use for , and notice that we were given the distance across the circle, which is its diameter. The radius is inches.) | |
Step 5. Solve. | |
Step 6. Check: We leave it to you to check your calculations. | |
Step 7. Answer the question. | The volume of the wrap is approximately cubic inches. |