- #1
pugtm
- 18
- 0
Homework Statement
x=2y^2
x=0
y=+-6
rotated around y
Homework Equations
integral 2pi*x(f(x)dx
The Attempt at a Solution
integral from -6 to 6 of 2pi*y*2y^2 dy
but i get something far less than the correct answer
A solid of revolution problem is a type of mathematical problem that involves rotating a two-dimensional shape around an axis to create a three-dimensional object. This is also known as a "revolved volume" or "solid of revolution".
The purpose of solving a solid of revolution problem is to calculate the volume, surface area, and other properties of the resulting three-dimensional object. This is useful in many fields such as engineering, physics, and geometry.
The steps to solve a solid of revolution problem are: 1. Identify the shape being rotated and the axis of rotation. 2. Set up the integral to find the volume or surface area of the object. 3. Evaluate the integral using appropriate integration techniques. 4. Simplify the solution and include units if necessary.
Some common shapes used in solid of revolution problems are circles, rectangles, and triangles. However, any two-dimensional shape can be used as long as it can be rotated around an axis.
The radius of rotation determines the size of the resulting solid. A larger radius will create a larger solid, while a smaller radius will create a smaller solid. Additionally, the radius can affect the shape of the resulting solid, with larger radii creating more rounded shapes and smaller radii creating more elongated shapes.