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In this lesson, we will learn how to determine the volume of a solid of revolution using the shell method for rotation around a vertical line.

Q1:

Find the volume of the solid obtained by rotating the region bounded by the curves 5 π¦ = π₯ , π¦ = 0 , π₯ = 3 , and π₯ = 4 about π₯ = 2 .

Q2:

Calculate the volume of a solid generated by rotating the region bounded by the curve π¦ = 5 π₯ β 2 2 , the π¦ -axis, and the straight line π¦ = 1 a complete revolution about the π¦ -axis.

Q3:

Calculate the volume of a solid generated by rotating the region bounded by the curve π¦ = 2 β 7 π₯ 2 and straight lines π₯ = 1 and π¦ = 4 a complete revolution about the π¦ -axis.

Q4:

Consider the region bounded by the curve π₯ π¦ = 4 and lines π¦ = 0 , π₯ = 1 , and π₯ = 2 . Find the volume of the solid obtained by rotating this region about π₯ = β 5 . Round your answer to two decimal places.

Q5:

Consider the region in the half plane π¦ β₯ 0 bounded by the curves π¦ = 4 π₯ 2 and π₯ + π¦ = 7 2 2 . Find the volume of the solid obtained by rotating this region about π¦ -axis. Round your answer to two decimal places.

Q6:

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve 4 π₯ + π¦ = 4 2 2 about π₯ = 2 .

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