### Finding the Volume of a Solid Formed by Revolution#### Problem:A region bounded by $ f(y) = y^2 $, $ y = 2 $, and $ x = 0 $ is shown below.Find the volume of the solid formed by revolving the region about the y-axis.![Graph of the Region](https://example.com/graph)#### Graph Explanation:The graph displays the parabola $ f(y) = y^2 $ in the xy-plane. The region of interest is bounded by the line $ y = 2 $ and the y-axis ($ x = 0 $).- The x-axis and y-axis are both labeled. - The parabola $ y^2 = x $ is outlined in green, extending into positive x and y quadrants.- The horizontal line $ y = 2 $ intersects the parabola.- The shaded region represents the area that will be revolved about the y-axis to form the solid.#### Choices for the Volume:- $ \frac{93}{5} \pi $- $ \frac{32}{3} \pi $- $ 10 \pi $- $ \frac{32}{5} \pi $

Answered: Image /qna-images/answer/77374063-0aab-41ee-b826-3e203639325d.jpg

Answered: A region bounded by f(y) = y², y = 2,…

A region bounded by f(y) = y², y = 2, and x = 0 is shown below. Find the volume of the solid formed by revolving the region about the y-axis. S432T345 1 42 3 4 5 6 7 8 9 93 ㅇㅈ ㅇㅠ 10 32 ·JT

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.5: Equations Of Lines

Problem 50E: The y-axis along with the graphs of y=-2x+7 and y=x+2 encloses a triangular region. Find the area of...

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Question

### Finding the Volume of a Solid Formed by Revolution

#### Problem:
A region bounded by $ f(y) = y^2 $, $ y = 2 $, and $ x = 0 $ is shown below.

Find the volume of the solid formed by revolving the region about the y-axis.

![Graph of the Region](https://example.com/graph)

#### Graph Explanation:
The graph displays the parabola $ f(y) = y^2 $ in the xy-plane. The region of interest is bounded by the line $ y = 2 $ and the y-axis ($ x = 0 $).

- The x-axis and y-axis are both labeled.
- The parabola $ y^2 = x $ is outlined in green, extending into positive x and y quadrants.
- The horizontal line $ y = 2 $ intersects the parabola.
- The shaded region represents the area that will be revolved about the y-axis to form the solid.

#### Choices for the Volume:
- $ \frac{93}{5} \pi $
- $ \frac{32}{3} \pi $
- $ 10 \pi $
- $ \frac{32}{5} \pi $

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