Volume Radius Problem: Solving with Cylindrical Method

In summary, the volume of the region between the curves y = x^2, y = 0, x = -2, and x = -1, revolved about the y-axis using the cylindrical method is calculated by finding the volumes of thin cylinders with a radius of x = 1 to x = 2. The assumption of being able to use the region in the first quadrant is correct, and the radius of the cylinders is simply x, as it is the distance from the origin. For further information on the cylindrical method, please refer to the fixed link provided.
  • #1
frozen7
163
0
The volume surrounded by y = x^2 , y=0, x=-2, x=-1 , revolved about y axis,by using cylindrical method.

The region is actually within x=-1 to -2 and it can actually same with x=1 to 2.

radius = 2-x
height = x^2

Is my assumption correct?
 
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  • #2
Your radius should simply be x. With limits of: x = 1 to 2

You assumption about being able to use the region in the 1st quadrant is correct, yes.
 
  • #3
How come the radius should be x?
 
  • #4
The radius should be x because the radius of the cylinder is the distance from the origin.
The volume of revolution is about the y-axis, which passes through the origin. And you are finding the volumes of all the thin cylinders starting with cylinders with a radius of x = 1 to x= 2.

See here for a further treatment of the cylindrical method.
 
Last edited:
  • #5
Something wrong with the link you have given.
 
  • #6
Sorry 'bout that. Forgot to add in the url.
The link is fixed now.
 

FAQ: Volume Radius Problem: Solving with Cylindrical Method

What is the "Volume Radius Problem" and why is it important?

The Volume Radius Problem is a mathematical problem that involves finding the volume of a cylinder using its radius. It is important because it has many real-world applications, such as calculating the volume of cylindrical objects like pipes, cans, or even planets.

How do you solve the Volume Radius Problem using the Cylindrical Method?

The Cylindrical Method involves using the formula V = πr2h, where V is the volume, r is the radius, and h is the height of the cylinder. Simply plug in the given values for r and h, and solve for V.

Are there any other methods for solving the Volume Radius Problem?

Yes, there are other methods such as the Spherical Method, which involves using the formula V = (4/3)πr3, and the Conical Method, which involves using the formula V = (1/3)πr2h. The method used depends on the shape of the object and the given information.

What units should be used for the radius and volume in the Volume Radius Problem?

The radius should be in units of length, such as meters, centimeters, or inches. The volume should be in units of cubic length, such as cubic meters, cubic centimeters, or cubic inches.

Can the Cylindrical Method be used to find the radius or height of a cylinder if the volume is known?

Yes, the formula V = πr2h can be rearranged to solve for either the radius or height if the other two values are known. This can be useful in real-world situations where one dimension of a cylindrical object is unknown.

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