Discussion
Revolving \( y = x \) from \( x = 0 \) to \( x = 3 \) about the \( x \)-axis gives a volume of
Answer: B
Apply the disc formula with \( y = x \):
\[ V \;=\; \pi\int_{0}^{3} x^{2}\,dx \;=\; \pi\left[\frac{x^{3}}{3}\right]_{0}^{3} \;=\; 9\pi. \]
The solid is a cone of radius three and height three, and the elementary formula \( \tfrac{1}{3}\pi r^{2}h = \tfrac{1}{3}\pi(9)(3) = 9\pi \) agrees
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