Volume part 2 Assignment.sagews

Volume, Part 2 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.

Note: You do not have to do any 3D plots.

Question 1

Use disks to find the volume of the solid obtained by rotating about the $x$-axis the region between $y=x^3$ and the $x$-axis from $x=0$ to $x=2$. [Answer: $\frac{128\pi}{7}$]

Question 2

Use disks to find the volume of the solid obtained by rotating about the $y$-axis the region between $y=2x$ and the $y$-axis from $y=0$ to $y=5$. [Answer: $\frac{125\pi}{12}$]

Question 3

Use washers to find the volume of the solid obtained by rotating about the $x$-axis the region between $y=\sqrt{x}$ and $y=x^3$ from $x=0$ to $x=1$. [Answer: $\frac{5\pi}{14}$]

Question 4

Use washers to find the volume of the solid obtained by rotating about the horizontal line $y=4$ the region between $y=x$ and $y=x^2$ from $x=0$ to $x=1$. [Answer: $\frac{6\pi}{5}$]

Question 5

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

Question 6

Use washers to find the volume of the solid obtained by rotating about the vertical line $x=3$ the region between $y=x+2$ and $y=\frac{1}{2}x^2+2$ from $x=0$ to $x=2$. [Answer:$\frac{8\pi}{3}$]

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.