Engineering Board Exam Reviewer · Applications: Volume, Arc Length, Surface Area · medium

The region bounded by y=x, x=0, and y=3 is revolved about the y-axis. Find the volume generated.

1. 9π 28.27
2. 3π
3. 27π
4. 9π/3

Answer

A. 9π 28.27

Solution

Since y=x, treat x as a function of y: V=π 03 y2,dy=π≤ft[y3/3 ]03=9π 28.27.

More Applications: Volume, Arc Length, Surface Area questions

1. Find the length of the arc of the curve y=x3/2 from x=0 to x=4.
2. Find the surface area generated by revolving the line y=x from x=0 to x=3 about the x-axis.
3. Find the length of the arc of y= 23x3/2 from x=0 to x=3.
4. The region bounded by y=x2, x=0, x=2, and the x-axis is revolved about the x-axis. Find the volume generated.
5. The region bounded by y=sqrt(x), x=0, and x=4 is revolved about the x-axis. Find the volume generated.

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