Joe_K said:For an answer, I came up with 5pi/4. Does this seem correct? Thanks!
tylerc1991 said:I am getting a different answer. What are your bounds? What is the integrand?
Joe_K said:My bounds were from 1 to 2.
What do you mean by "with a height of 1" ?Joe_K said:Homework Statement
Find the volume obtained by rotating the solid about the specified line.
y=2-(1/2)x, y=0, x=1, x=2, about the x-axis.
Homework Equations
I used the disk method
The Attempt at a Solution
I drew a sketch and used disk method. For the radius I used 2-(1/2)x with a height of 1, and integrated. For an answer, I came up with 5pi/4. Does this seem correct? Thanks!
SammyS said:What do you mean by "with a height of 1" ?
What function did you integrate?
Joe_K said:For the integrand I just had pi*2-(1/2)x*1 dx
tylerc1991 said:The area of one of the disks is going to be [itex]\pi \cdot (2 - \frac{1}{2} x)^2[/itex]. What happens when we sum those disks from [itex]x = 1[/itex] to [itex]x = 2[/itex]?
Joe_K said:I think I forgot to square the radius when I originally did it. I redid the problem and came up with 19pi/12. Is this still wrong?
A "Solid of Revolution Problem" is a mathematical concept that involves rotating a two-dimensional shape around an axis to create a three-dimensional solid. This problem is often encountered in calculus and is used to calculate the volume and surface area of various objects.
To solve a Solid of Revolution Problem, you must first identify the axis of rotation and the boundaries of the shape. Then, you can use integration techniques to find the volume or surface area of the resulting solid. This process may require the use of different integration methods, such as the disk method or the shell method.
Yes, a Solid of Revolution Problem can have a curved axis. In fact, this type of problem is commonly encountered in real-world scenarios, such as finding the volume of a wine barrel or the surface area of a water tower. In these cases, the integration methods may need to be adjusted to accommodate the curved axis.
Solid of Revolution Problems have many practical applications in fields such as engineering, physics, and architecture. Some examples include calculating the volume of a cylindrical tank, finding the surface area of a rollercoaster track, and determining the moment of inertia of a rotating object.
While Solid of Revolution Problems can be applied to a wide range of shapes and objects, they do have some limitations. For instance, this method may not be suitable for objects with irregular shapes or non-uniform density. In these cases, alternative methods, such as the Pappus's centroid theorem, may be used to calculate the volume or surface area.