Finding Volume by Cross Section Area

In summary, the conversation discusses finding the volume of a figure with curved boundaries using the area of triangular cross sections. The cross sections are equilateral triangles and the formula for their area is given. The conversation also touches on the use of a sketch to visualize the problem and the importance of considering the interval of integration.
  • #1
heather7113
3
0
I need to find the volume of this figure y=sinx, y=sinx + 2, x=4, x=-4 using the area of triangular cross sections. i don't really know where to start...how to find the formula for area of cross section etc. HELP!
 
Physics news on Phys.org
  • #2
heather7113 said:
I need to find the volume of this figure y=sinx, y=sinx + 2, x=4, x=-4 using the area of triangular cross sections. i don't really know where to start...how to find the formula for area of cross section etc. HELP!

What kind of triangle cross sections? Right? Equilateral? Have you drawn a sketch of this? Do you know the formula for the area of a triangle? A sketch will help.
 
  • #3
The cross sections are equilateral triangles. And I have drawn a sketch - I'm just not sure what the integral should be - like what is the formula for the base of the triangle. I know the formula is sgrt 3 x b / 4 I just don't really know what to plug in and what the numbers should be...?
 
  • #4
heather7113 said:
The cross sections are equilateral triangles. And I have drawn a sketch - I'm just not sure what the integral should be - like what is the formula for the base of the triangle. I know the formula is sgrt 3 x b / 4 I just don't really know what to plug in and what the numbers should be...?

Isn't the base of the triangle just the positive difference between the values of the two curves at position x? And the slice has thickness dx. At least that is so on the interval [itex](0,\pi)[/itex]. Outside of that interval you have to be careful because the curves cross each other at 0 and [itex]\pi[/itex].
 
  • #5
Thanks. Thats what I was thinking, I just wasn't sure...
 

1. What is the formula for finding volume by cross section area?

The formula for finding volume by cross section area is V = A * L, where V is the volume, A is the cross section area, and L is the length of the object.

2. How do you find the cross section area?

The cross section area can be found by measuring the length and width of the object and then multiplying them together. It can also be found by using geometric formulas such as the area of a circle or triangle.

3. Can you find the volume by cross section area for any 3D object?

Yes, the volume by cross section area can be found for any 3D object as long as the cross section area remains constant throughout the length of the object.

4. What units are used for volume and cross section area?

The units for volume and cross section area will depend on the units used for length. For example, if length is measured in meters, then volume will be in cubic meters and cross section area will be in square meters.

5. How accurate is the volume by cross section area method?

The accuracy of the volume by cross section area method will depend on the accuracy of the measurements used for length and cross section area. The smaller the intervals used for measuring, the more accurate the result will be.

Similar threads

Replies
2
Views
1K
Replies
4
Views
323
  • Calculus
Replies
2
Views
1K
Replies
2
Views
243
  • Calculus
Replies
16
Views
450
  • Introductory Physics Homework Help
Replies
25
Views
1K
Replies
20
Views
2K
  • Calculus
Replies
3
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
9
Views
2K
  • Mechanical Engineering
Replies
22
Views
443
Back
Top