- #1
songoku
- 2,328
- 336
- Homework Statement
- Please see below
- Relevant Equations
- Double Integral
Triple Integral
Cylindrical coordinate
Spherical coordinate
My attempt:
The shape of the hyperboloid would be like this:
If the hyperbolod is cut by plane z = d, the intersection would be a ellipse. Projecting the intersection to xy - plane, I think I get:
$$-2\leq x \leq 2$$
$$-b\sqrt{1-\frac{x^2}{a^2}} \leq y \leq b\sqrt{1-\frac{x^2}{a^2}}$$
So the volume would be:
$$V=2 \times \int_{-2}^{2} \int_{-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}} \left(c\sqrt{\frac{x^2}{a^2}+\frac{y^2}{b^2}-1}\right)dydx$$
Is this correct?
Thanks
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