What is a solid of revolution in calculus?
If a region in the plane is revolved about a line in the same plane, the resulting object is known as a solid of revolution. For example, a solid right circular cylinder can be generated by revolving a rectangle.
How do you find the solid of revolution?
To get a solid of revolution we start out with a function, y=f(x) y = f ( x ) , on an interval [a,b] . We then rotate this curve about a given axis to get the surface of the solid of revolution.
How can the formula for the volume of a solid of revolution be obtained?
If the cross sections of the solid are taken parallel to the axis of revolution, then the cylindrical shell method will be used to find the volume of the solid. If the cylindrical shell has radius r and height h, then its volume would be 2π rh times its thickness.
Which solid is a solid of revolution?
In geometry, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line (the axis of revolution) that lies on the same plane. The surface created by this revolution and which bounds the solid is the surface of revolution.
Which of the following is a solid of revolution?
A cone is solid of revolution generated by rotation of a right triangle around one of its legs as the axis of revolution. A cylinder is solid of revolution generated by rotation of rectangular around one of its sides as the axis of revolution.
What are various solids of revolution?
Solid of Revolution
| solid | |
|---|---|
| conical frustum | 0 |
| cylinder | 0 |
| oblate spheroid | |
| prolate spheroid |
What is the shape of solid?
A 3-D shape, or solid, is an object with three dimensions: length, width, and height. Solids have surface areas (the outside of the object) and volumes (the amount of space inside the object). Many common solids are polyhedrons, which are three-dimensional shapes with flat surfaces and straight edges.
Is disk and washer method the same?
Washer Method A washer is like a disk but with a center hole cut out. The formula for the volume of a washer requires both an inner radius r1 and outer radius r2. We’ll need to know the volume formula for a single washer.
Which solid is not a solid of revolution?
The pyramid and cube do not have circular cross sections, so these are not solids of revolution.
What are the solids of revolution except?
A polyhedron may be regular or irregular. Regular polyhedrons have equal and regular polygons e.g. cube and tetrahedron etc. ∴ Pyramid is not solid of revolution.