Determine Volume V of the figure

Question

Answer: V=848 and m=6.6kg.

please help me to solve problem with explanation?

Answer 1

You will need the concept of volume of revolution using integration.

The slope of the graph is $\frac{9}{6}=\frac{3}{2}$. You can then shift the graph near to the $y$-axis to get the equation $y=\frac{3}{2}x+2$.

So the desired volume of revolution $V$ is (I will leave out some explanations for you to think about) $$\left\{\pi\int_{0}^{6}\left(\frac{3}{2}x+2\right)^2dx\right\}-\left\{\pi\cdot2^2\cdot6\right\}=270\pi\approx848$$

To get the desired mass $m$, I guess you should know what to do...