Let R be the region bounded by the curves y = x³, y = 8, x = 0. 1. Sketch the region and find the area. Write your answer in simplest fractional form. 2. Sketch the solid you obtain by rotating the region R about the x-axis. 3. Find the volume of the solid obtained by rotating the region R about the x-axis using the disk/washer method. Write the formula you are using. Write your answer in terms of л. Draw the approximating rectangle that you rotate. 4. Find the volume of the solid obtained by rotating the region R about the x-axis using the shell method. Write the formula you are using. Write your answer in terms of 7. Draw the approximating rectangle that you rotate. 5. Which method did you find easier and why? [There is no wrong answer for what you find easier, but explain.] 6. Sketch the solid you obtain by rotating the region R about the y-axis. 7. Find the volume of the solid obtained by rotating the region R about the y-axis using the disk/washer method. Write the formula you are using. Write your answer in terms of 7. Draw the approximating rectangle that you rotate. 8. Find the volume of the solid obtained by rotating the region R about the y-axis using the shell method. Write the formula you are using. Write your answer in terms of π. Draw the approximating rectangle that you rotate. 9. Which method did you find easier and why? [There is no wrong answer for what
Let R be the region bounded by the curves y = x³, y = 8, x = 0. 1. Sketch the region and find the area. Write your answer in simplest fractional form. 2. Sketch the solid you obtain by rotating the region R about the x-axis. 3. Find the volume of the solid obtained by rotating the region R about the x-axis using the disk/washer method. Write the formula you are using. Write your answer in terms of л. Draw the approximating rectangle that you rotate. 4. Find the volume of the solid obtained by rotating the region R about the x-axis using the shell method. Write the formula you are using. Write your answer in terms of 7. Draw the approximating rectangle that you rotate. 5. Which method did you find easier and why? [There is no wrong answer for what you find easier, but explain.] 6. Sketch the solid you obtain by rotating the region R about the y-axis. 7. Find the volume of the solid obtained by rotating the region R about the y-axis using the disk/washer method. Write the formula you are using. Write your answer in terms of 7. Draw the approximating rectangle that you rotate. 8. Find the volume of the solid obtained by rotating the region R about the y-axis using the shell method. Write the formula you are using. Write your answer in terms of π. Draw the approximating rectangle that you rotate. 9. Which method did you find easier and why? [There is no wrong answer for what
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.CR: Review Exercises
Problem 21CR: Find the volume of the solid of revolution that results when a right triangle with legs of lengths 5...
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solve questions 3, 4,5, 7, 8, and 9
![Let R be the region bounded by the curves y = x³, y = 8, x = 0.
1. Sketch the region and find the area. Write your answer in simplest fractional form.
2. Sketch the solid you obtain by rotating the region R about the x-axis.
3. Find the volume of the solid obtained by rotating the region R about the x-axis
using the disk/washer method. Write the formula you are using. Write your answer
in terms of л. Draw the approximating rectangle that you rotate.
4. Find the volume of the solid obtained by rotating the region R about the x-axis
using the shell method. Write the formula you are using. Write your answer in
terms of 7. Draw the approximating rectangle that you rotate.
5. Which method did you find easier and why? [There is no wrong answer for what
you find easier, but explain.]
6. Sketch the solid you obtain by rotating the region R about the y-axis.
7. Find the volume of the solid obtained by rotating the region R about the y-axis
using the disk/washer method. Write the formula you are using. Write your answer
in terms of 7. Draw the approximating rectangle that you rotate.
8. Find the volume of the solid obtained by rotating the region R about the y-axis using
the shell method. Write the formula you are using. Write your answer in terms of
π. Draw the approximating rectangle that you rotate.
9. Which method did you find easier and why? [There is no wrong answer for what](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fceff0366-e600-4c18-833e-ef8248db6a44%2F4c66fb88-8618-4040-9fa4-b37c04d16b38%2F8txju7d_processed.png&w=3840&q=75)
Transcribed Image Text:Let R be the region bounded by the curves y = x³, y = 8, x = 0.
1. Sketch the region and find the area. Write your answer in simplest fractional form.
2. Sketch the solid you obtain by rotating the region R about the x-axis.
3. Find the volume of the solid obtained by rotating the region R about the x-axis
using the disk/washer method. Write the formula you are using. Write your answer
in terms of л. Draw the approximating rectangle that you rotate.
4. Find the volume of the solid obtained by rotating the region R about the x-axis
using the shell method. Write the formula you are using. Write your answer in
terms of 7. Draw the approximating rectangle that you rotate.
5. Which method did you find easier and why? [There is no wrong answer for what
you find easier, but explain.]
6. Sketch the solid you obtain by rotating the region R about the y-axis.
7. Find the volume of the solid obtained by rotating the region R about the y-axis
using the disk/washer method. Write the formula you are using. Write your answer
in terms of 7. Draw the approximating rectangle that you rotate.
8. Find the volume of the solid obtained by rotating the region R about the y-axis using
the shell method. Write the formula you are using. Write your answer in terms of
π. Draw the approximating rectangle that you rotate.
9. Which method did you find easier and why? [There is no wrong answer for what
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