Calc 2 solids of revolution help

You should have used √(a^2-x^2)/tan(60) instead of √(a^2-x^2)/tan(30) in your formula.In summary, a solid lies between planes perpendicular to the x-axis at x=-a and x=a for values of a>0. The cross-sections perpendicular to the x-axis between these planes are semicircles with equations y=√(a^2-x^2) and y=-√(a^2-x^2). For the given case of a=7, the cross-sections are equilateral triangles with bases in the x-y plane. The formula for the area A(x) of the cross-section at location x is (
  • #1
kellyb1ll
3
0
A solid lies between planes perpendicular to the x-axis at x=-a and x=a for values of a>0 to be given below in parts (i) and (ii). In each case the cross-sections perpendicular to the x-axis between these planes run from the semicircle y=√(a^2-x^2) to the semicircle
y=-√(a^2-x^2).

If a=7 and the cross-sections are equilateral triangles with bases in the x-y plane, find a formula for the area A(x) of the cross-section at location x.


For the base i used 2*√(a^2-x^2), for the height i used √(a^2-x^2)/tan(30). so i get
(a^2-x^2)/tan(30) as an answer, which is not right. what am i doing wrong i can't seem to figure it out.

i uploaded a picture of what the problem gave me if it helps.
THANKS!
 

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  • #2
Why do you think that is not right?
 
  • #3
its a problem on my online homework and when i type in that answer it says its wrong
 
  • #4
You made a mistake finding the height of the triangle.
 

FAQ: Calc 2 solids of revolution help

What is a solid of revolution?

A solid of revolution is a three-dimensional shape that is created by rotating a two-dimensional shape around a fixed axis. This can be visualized as a 3D object formed by sweeping a 2D shape around a central line.

What are the key concepts in Calculus 2 related to solids of revolution?

Some key concepts in Calculus 2 related to solids of revolution include integration, the disk method, the washer method, and the shell method. These concepts are used to calculate the volume of a solid of revolution.

How do I find the volume of a solid of revolution?

The volume of a solid of revolution can be found using integration and one of the three methods mentioned above (disk, washer, or shell). The steps for finding the volume will depend on the shape of the solid and the method being used.

Can you provide an example problem of finding the volume of a solid of revolution?

Sure! Let's say we have the function y = x^2 and we want to rotate it around the x-axis from x=0 to x=2. We can use the disk method and the formula V = π∫[a,b] (f(x))^2 dx to find the volume. Plugging in our values, we get V = π∫[0,2] (x^2)^2 dx = π∫[0,2] x^4 dx = 32π/5.

Are there any common mistakes to avoid when working with solids of revolution?

Yes, there are some common mistakes to avoid when working with solids of revolution. Some include not using the correct formula for the method being used, not setting up the limits of integration correctly, and not properly identifying the shape being rotated. It is important to carefully read and understand the problem and double check your calculations to avoid these mistakes.

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