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Question

# Use integration to compute the volume of a right circular cone generated by revolving the ordinate set of a linear function f(x)=cx over the interval $0 \leq x \leq b$. Show that the result is one-third the area of the base times the altitude of the cone.

Solution

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For the purpose of making it clear to you, a graph is attached below. We can see that we are rising in the $y$ direction $r$ units and moving in the $x$-axis $h$ units, so the equation of our lines would be given by $y=\dfrac{r}{h} x$. In our problem, $h=b$ and $c=\dfrac{r}{h}=\dfrac{r}{b}$.

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