Review question

# What volume is generated when $y = ax - x^2$ is rotated about the x-axis? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5007

## Question

The curve $y = ax - x^2$ cuts the $x$-axis at the points $(0,0)$ and $(a,0)$. The area enclosed between the curve and the $x$-axis is $36$ square units. Calculate the value of $a$.

With this value of $a$ find, as a multiple of $\pi$, the volume obtained when the above area is rotated through $4$ right angles about the $x$-axis.