May I ask how to calculate the volume of a cone after it is cut by a plane?
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As shown in the figure, a cone is cut by a plane that is perpendicular to the base plane of the cone. How can the remaining volume be calculated? Software can be used too.
Draw an auxiliary line at the cross-section parallel to the uncut side of the cone; this divides the irregular shape into a triangle and a pyramid. If the necessary data are known, the volume can be calculated
This seems to be a high school math problem. The second floor is correct.
This post was last edited by qugd on 2018-2-7 20:40. Do you confirm that your approach works for calculation? How can your auxiliary line be parallel to the uncut side of the cone? What does the triangle you mentioned being cut out look like? The uncut side can be regarded as a part of the lateral surface of a frustum, which is an arc-shaped surface. How can a straight line be parallel to an arc-shaped surface? It’s better for you to first sort out your knowledge of solid geometry; don’t talk nonsense if you don’t understand it. It’s best to first describe things in a way that others can understand. Please list a calculation formula for everyone to see; these references can be replaced with letters.
This post was last edited by qugd on 2018-2-7 at 20:45. It is suggested that the original poster consult an engineering mathematics handbook; it seems to be composed of a small cone and a frustum, with part of the frustum missing – that missing part is the section that has been cut off. This divides it into three parts, and then the volume of any two of these parts can be calculated. I remember similar calculations in the Handbook of Engineering Mathematics. Refer to the figure below:
By creating the model directly with 3D software, it’s easy to obtain the volume; calculating it manually is too troublesome