Volume part 3 Assignment.sagews

Volume, Part 3 Assignment

Question 0

Watch the lecture video here.

Did you watch the video? [Type yes or no.]

For each question below:

• Draw a graph of the region to be rotated.

• Find the volume of the solid.

Question 1

Use cylindrical shells to find the volume of the solid obtained by rotating around the $y$-axis the region between $y=(x-1)(x-3)^2$ and the $x$-axis from $x=1$ to $x=3$. [Answer: $\frac{24\pi}{5}$]

Question 2

Use cylindrical shells to find the volume of the solid obtained by rotating around the $y$-axis the region between $y=x$ and $y=x^2$ from $x=0$ to $x=1$. [Answer: $\frac{\pi}{6}$]

Question 3

Use cylindrical shells to find the volume of the solid obtained by rotating around the vertical line $x=2$ the region between $y=x-x^2$ and the $x$-axis from $x=0$ to $x=1$. [Answer: $\frac{\pi}{2}$]

Question 4

Use cylindrical shells to find the volume of the solid obtained by rotating around the $x$-axis the region between $y=x$ and $y=x^2$ from $x=0$ to $x=1$. [Answer: $\frac{2\pi}{15}$]

Question 5

Use cylindrical shells to find the volume of the solid obtained by rotating around the horizontal line $y=5$ the region between $y=x+2$ and $y=\frac{1}{2}x^2+2$ from $x=0$ to $x=2$. [Answer: $\frac{44\pi}{15}$]

This material was developed by Aaron Tresham at the University of Hawaii at Hilo and is
licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.