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For the region bounded by y=x, the x-axis, and x = 4, determine which of the following is greater: the volume of the solid generated when the region is revolved about the x-axis or about the y-axis. When the region is revolved about the x-axis, the volume is (Type an exact answer, using as needed.) When the region is revolved about the y-axis, the volume is. (Type an exact answer, using as needed.) Which volume is greater? OA. The volume about the y-axis is greater. OB. The volume about the x-axis is greater. OC. The volumes are equal. C...

For the region bounded by y=x, the x-axis, and x = 4, determine which of the following is greater: the volume of the solid generated when the region is revolved about the x-axis or about the y-axis. When the region is revolved about the x-axis, the volume is (Type an exact answer, using as needed.) When the region is revolved about the y-axis, the volume is. (Type an exact answer, using as needed.) Which volume is greater? OA. The volume about the y-axis is greater. OB. The volume about the x-axis is greater. OC. The volumes are equal. C...

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
For the region bounded by \( y = x \), the x-axis, and \( x = 4 \), determine which of the following is greater: the volume of the solid generated when the region is revolved about the x-axis or about the y-axis. When the region is revolved about the x-axis, the volume is \(\_\_\_\). (Type an exact answer, using \(\pi\) as needed.) When the region is revolved about the y-axis, the volume is \(\_\_\_\). (Type an exact answer, using \(\pi\) as needed.) Which volume is greater? - A. The volume about the y-axis is greater. - B. The volume about the x-axis is greater. - C. The volumes are equal.
Transcribed Image Text:For the region bounded by \( y = x \), the x-axis, and \( x = 4 \), determine which of the following is greater: the volume of the solid generated when the region is revolved about the x-axis or about the y-axis. When the region is revolved about the x-axis, the volume is \(\_\_\_\). (Type an exact answer, using \(\pi\) as needed.) When the region is revolved about the y-axis, the volume is \(\_\_\_\). (Type an exact answer, using \(\pi\) as needed.) Which volume is greater? - A. The volume about the y-axis is greater. - B. The volume about the x-axis is greater. - C. The volumes are equal.
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