Discussion
The volume of the tetrahedron bounded by \( x + y + z = 1 \) and the coordinate planes is
Answer: B
Integrate the height \( z = 1 - x - y \) over the triangle \( x + y \le 1 \) in the base plane:
\[ V \;=\; \int_{0}^{1}\!\!\int_{0}^{1-x}\left(1 - x - y\right)dy\,dx \;=\; \int_{0}^{1}\frac{(1-x)^{2}}{2}\,dx \;=\; \frac{1}{6}. \]
The elementary formula \( \tfrac{1}{3}\times\text{base}\times\text{height} = \tfrac{1}{3}(\tfrac{1}{2})(1) \) agrees
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