Finding Volume by Cross Section Area

Click For Summary
To find the volume of the figure defined by y=sinx, y=sinx + 2, x=4, and x=-4 using equilateral triangular cross sections, the base of each triangle is determined by the positive difference between the two curves at a given x. The thickness of each slice is dx, and the integral must account for the intervals where the curves intersect, specifically between 0 and π. A sketch of the figure can aid in visualizing the problem and clarifying the dimensions of the triangles. The area of each triangular cross section can be calculated using the formula (sqrt(3)/4) * b^2, where b is the base length. Properly setting up the integral with these parameters will yield the desired volume.
heather7113
Messages
3
Reaction score
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
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.
 
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...?
 
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 (0,\pi). Outside of that interval you have to be careful because the curves cross each other at 0 and \pi.
 
Thanks. Thats what I was thinking, I just wasn't sure...
 

Thread 'How does this derivative work? And why the speed of light remains?'

Relativistic Momentum, Mass, and Energy Momentum and mass (...), the classic equations for conserving momentum and energy are not adequate for the analysis of high-speed collisions. (...) The momentum of a particle moving with velocity ##v## is given by $$p=\cfrac{mv}{\sqrt{1-(v^2/c^2)}}\qquad{R-10}$$ ENERGY In relativistic mechanics, as in classic mechanics, the net force on a particle is equal to the time rate of change of the momentum of the particle. Considering one-dimensional...
View full post »

Similar threads

MHB What is the Volume of a Solid with Squares as Cross Sections?
  • · Replies 2 ·
Replies
2
Views
2K
High School How to find the objects' areas in this photo in mm^2?
  • · Replies 14 ·
Replies
14
Views
2K
High School Volume of paraboloid in a cylinder
  • · Replies 2 ·
Replies
2
Views
3K
High School Having trouble deriving the volume of an elliptical ring toroid
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Why is there such a difference between the total cross-section data? (simulation vs. experiment)
  • · Replies 1 ·
Replies
1
Views
717
High School Question about units for "area under curve"
  • · Replies 2 ·
Replies
2
Views
3K
Misc. Yarn cross-section and path length
  • · Replies 3 ·
Replies
3
Views
658
Flowrate through an elliptical cross section of an oblique liquid jet
  • · Replies 11 ·
Replies
11
Views
2K
High School Question about volume of a sphere
  • · Replies 16 ·
Replies
16
Views
3K