Determine the volume V generated by revolving the quarter-circular area about the z-axis through an angle of 90°. 1.9a

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter15: Fluid Mechanics
Section: Chapter Questions
Problem 9CQ
Question
100%

I got a volume of 9.7285 a^3 and its incorrect. How do I solve this?

**Problem Statement:**

Determine the volume \( V \) generated by revolving the quarter-circular area about the z-axis through an angle of \( 90^\circ \).

**Diagram Explanation:**

The diagram shows a quarter-circular area being revolved around the z-axis. This forms a three-dimensional shape, which resembles a quarter-cylinder or a curved section of a cylindrical shell. The dimensions given in the diagram are:
- The radius of the quarter-circle is labeled as \( a \).
- The height along the z-axis is \( 1.9a \).

The axes are labeled as x, y, and z.

**Answer:**

\[ V = 9.7285 \, a^3 \]
Transcribed Image Text:**Problem Statement:** Determine the volume \( V \) generated by revolving the quarter-circular area about the z-axis through an angle of \( 90^\circ \). **Diagram Explanation:** The diagram shows a quarter-circular area being revolved around the z-axis. This forms a three-dimensional shape, which resembles a quarter-cylinder or a curved section of a cylindrical shell. The dimensions given in the diagram are: - The radius of the quarter-circle is labeled as \( a \). - The height along the z-axis is \( 1.9a \). The axes are labeled as x, y, and z. **Answer:** \[ V = 9.7285 \, a^3 \]
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