Question

sketch and describe the solid that is produced when the region enclosed by y=4, x=0, and y=2x is rotated around the the y axis. then find the volume of the solid

Answer 1

rotation

the volume of the cone is

$V=\frac{\pi\times r^2\times h}{3}$

where the radio is 2 and the height is 4

$V=\frac{\pi\times(2)^2\times(4)}{3}$$\begin{gathered} \frac{\pi\times4\times4}{3} \\ =\frac{16\pi}{3}\approx16.75 \end{gathered}$