Volume of Revolution: Find the Volume with Maple Help

In summary, the question asks for the volume of a solid generated by rotating the finite plane region bounded by the curve x*y=1 and the straight line 2x+2y=5 about that line. To solve this, one must first find the intersection between the hyperbola xy=1 and the line 2x+2y=5. Then, the distance between the line and hyperbola must be found along a line perpendicular to 2x+2y=5. This can be done by finding the slope of 2x+2y=5 (-1) and using the equation y=x+b for some b.
  • #1
wedontneed
1
0
here is the question:

The finite plane region bounded by the curve x*y=1 and the straight line
2x+2y=5 is rotated about that line to generate a solid of revolation. Find the volume of solid.

İ have to do this on mapple can someone help me how can i do this.
 
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  • #2
Have you drawn the graph? In particular you will need to find where the hyperbola xy= 1 and 2x+ 2y= 5. What x satisfies 2x+ 2/x= 5? You might also want to find the distance between the line and hyperbola measured along the line perpendicular to 2x+ 2y= 5. Since 2x+2y= 5 has slope -1, any line perpendicular to that has equation y= x+ b for some b.
 

1. How do I use Maple to find the volume of revolution?

To find the volume of revolution using Maple, you will need to use the "revolve" command. This command takes in the function, the variable of integration, the lower and upper bounds, and the axis of revolution as arguments. For example, the command "revolve(x^2, x, 0, 1, y)" would find the volume of revolution when the function x^2 is revolved around the y-axis between x = 0 and x = 1.

2. Can I use Maple to find the volume of revolution for three-dimensional shapes?

Yes, Maple can be used to find the volume of revolution for three-dimensional shapes. You will need to use the "revolve" command with multiple variables and bounds to define the shape. Keep in mind that the axis of revolution can also be a function of the variables.

3. How accurate are the volume calculations in Maple?

The accuracy of the volume calculations in Maple depends on the number of decimal places you specify in your calculations. By default, Maple will display the result to 10 decimal places. You can increase the accuracy by using the "evalf" command and specifying the desired number of decimal places. Keep in mind that the accuracy also depends on the accuracy of the function being integrated.

4. Can I visualize the volume of revolution in Maple?

Yes, Maple has a built-in feature called "plotrevolve" that allows you to visualize the volume of revolution. This command takes in the same arguments as the "revolve" command and creates a 3D plot of the shape and its revolution. This can help you better understand the shape and the volume calculation.

5. How can I check my results for the volume of revolution in Maple?

In order to check your results, you can use the "int" command in Maple to calculate the volume of revolution using the same function, bounds, and axis of revolution. You can then compare the result with your initial calculation. Additionally, you can also use the "int" command to find the volume of revolution for simpler shapes, such as cylinders or cones, and compare the results to ensure accuracy.

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