Finding the Volume of a Cone
Learning Outcomes
- Find the volume of cones
Volume of a Cone
For a cone with radius [latex]r[/latex] and height [latex]h[/latex] .example
Find the volume of a cone with height [latex]6[/latex] inches and radius of its base [latex]2[/latex] 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 [latex]V[/latex] = volume. |
Step 4. Translate. Write the appropriate formula. Substitute. (Use [latex]3.14[/latex] for [latex]\pi [/latex] ) | [latex]V=\Large\frac{1}{3}\normalsize\pi {r}^{2}h[/latex] [latex]V\approx \Large\frac{1}{3}\normalsize 3.14{\left(2in\right)}^{2}\left(6in\right)[/latex] |
Step 5. Solve. | [latex]V\approx 25.12in^3[/latex] |
Step 6. Check: We leave it to you to check your calculations. | |
Step 7. Answer the question. | The volume is approximately [latex]25.12[/latex] cubic inches. |
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[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 [latex]8[/latex] inches tall and [latex]5[/latex] 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 [latex]3.14[/latex] for [latex]\pi [/latex] , and notice that we were given the distance across the circle, which is its diameter. The radius is [latex]2.5[/latex] inches.) | [latex]V=\Large\frac{1}{3}\normalsize\pi {r}^{2}h[/latex] [latex]V\approx \Large\frac{1}{3}\normalsize 3.14{\left(2.5in\right)}^{2}\left(8in\right)[/latex] |
Step 5. Solve. | [latex]V\approx 52.33in^3[/latex] |
Step 6. Check: We leave it to you to check your calculations. | |
Step 7. Answer the question. | The volume of the wrap is approximately [latex]52.33[/latex] cubic inches. |
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[ohm_question]146820[/ohm_question]Contribute!
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- Question ID 146820, 146818. Authored by: Lumen Learning. License: CC BY: Attribution.
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- Ex: Determine Volume of a Cone. Authored by: James Sousa (amthispower4u.com). License: CC BY: Attribution.
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- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].