Evaluate the volume of the solid:
$$V=\{(x, y, z)\in \mathbb{R}^3: x \in [-1, 1], \;\; y^2+ z^2 \leq x^2$$
Solution
We simply note that this solid is actually is a cone. Hence:
$$V=\frac{1}{3}\pi r^2 h = \frac{2\pi}{3}$$
since the radius is simply $1$ and the height is $2$.
One can also do this using integral calculus. We leave the details to the reader.
$$V=\{(x, y, z)\in \mathbb{R}^3: x \in [-1, 1], \;\; y^2+ z^2 \leq x^2$$
Solution
We simply note that this solid is actually is a cone. Hence:
$$V=\frac{1}{3}\pi r^2 h = \frac{2\pi}{3}$$
since the radius is simply $1$ and the height is $2$.
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