Volume of Frustum of a Right Circular Cone

In summary, the conversation is about finding the volume of a frustum of a right circular cone using the Method of Washers and the Method of Cylindrical Shells. The person provides an image of the 3D object and their attempt at solving the problem using the Method of Washers, which yielded an incorrect answer. They mention not attempting the Method of Cylindrical Shells due to having only one attempt left. The person asks for assistance in identifying the mistake in their work.
  • #1
skyturnred
118
0

Homework Statement



A frustum of a right circular cone with height h, lower base radius R, and top radius r. Find it's volume.

Homework Equations



We are currently learning the Method of Washers and the Method of Cylindrical Shells so I believe we are supposed to use this somehow.

The Attempt at a Solution



Here is an image of the 3d object if it helps!

KibfO.png


If the above doesn't work use this link:

http://i.imgur.com/KibfO.png

The following is my work. The first image is my work trying method of washers. The answer I obtained is wrong. The second image is my work trying cylindrical shells. I have not attempted this answer because I only have one attempt left. Please let me know where I am going wrong!

Method of washers:

sCONu.jpg

http://i.imgur.com/sCONu.jpg

Cylindrical Shells:

yKUmH.jpg

http://i.imgur.com/yKUmH.jpg

Thank you SO much in advance for your help!

***I ended up getting the answer. After re-checking my work (again) I found that I accidentally dropped an x.
 

Attachments

  • KibfO.png
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  • sCONu.jpg
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  • KibfO.png
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  • KibfO.png
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  • sCONu.jpg
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Last edited:
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  • #2


can you explain your work in the second picture? thanks!
 

1. What is a frustum of a right circular cone?

A frustum of a right circular cone is a 3D geometric shape that is formed when the top portion of a cone is cut off by a plane parallel to its base. It has a circular base and a circular top that are connected by a curved surface.

2. How is the volume of a frustum of a right circular cone calculated?

The formula for calculating the volume of a frustum of a right circular cone is V = (1/3)πh(R2 + Rr + r2), where h is the height of the frustum, R is the radius of the base, and r is the radius of the top.

3. Can the volume of a frustum of a right circular cone be negative?

No, the volume of a frustum of a right circular cone cannot be negative. Volume is a measure of the space occupied by an object, and it cannot have a negative value.

4. What are the units for measuring the volume of a frustum of a right circular cone?

The units for measuring the volume of a frustum of a right circular cone will depend on the units used for the dimensions of the cone. For example, if the height is measured in meters and the radii are measured in centimeters, the volume will be in cubic meters.

5. How is the volume of a frustum of a right circular cone related to the volume of a cone?

The volume of a frustum of a right circular cone is a portion of the volume of a cone. If the top portion of a cone is cut off by a plane that is parallel to its base, the remaining volume will be the volume of the frustum. The volume of the frustum is calculated by subtracting the volume of the smaller cone (formed by the top portion) from the volume of the larger cone (original cone).

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