Solids of well-known cross sections help
I'm making a model of a solid that has the cross-section of an altitude of the hypotenuse of an isosceles right triangle. Viewed from the "side", the model would look like this, with the solid line dividing the triangle as the plane it is going through.
This is my math:
My equation is x2 + y2 = e2
A = 1/2bh
Therefore, the base of the triangle I will be using = 2√3√e2-x2
And the height = x
so...
A = 1/2 ( 2 * x * √3√e2-x2
And to find the volume, the equation would be
√3∫-ee x√e2-x2dx
Right? But when I put it into my calculator, I get that the volume = 0.
What am I doing wrong? Please check my work. Thank you in advance!
This is my math:
My equation is x2 + y2 = e2
A = 1/2bh
Therefore, the base of the triangle I will be using = 2√3√e2-x2
And the height = x
so...
A = 1/2 ( 2 * x * √3√e2-x2
And to find the volume, the equation would be
√3∫-ee x√e2-x2dx
Right? But when I put it into my calculator, I get that the volume = 0.
What am I doing wrong? Please check my work. Thank you in advance!