Question

The volume of solid formed by revolving the line $y=7x$ along the x-axis bounded by $x=-1$ and $x=1$ is be equal to $\frac{a\pi }{3}$. What is the value of a?

Answer 1

Volume of small disc

$\Rightarrow$ $\pi y^{2}dx$

$=\pi {\int }_{-1}^1{y}^{2}dx$

$=\pi {\int }_{-1}^{1}49x^{2}dx$

$=49\pi {\int }_{-1}^1\frac{x^3}{3}$

$=\frac{49\pi x^2}{3}$

$=\frac{98\pi }{3}$