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In this lesson, we will learn how to find the volume of a solid by revolution of a two-dimensional region about the y-axis using the disk method.

Q1:

The region bounded by the curves π₯ = 3 β π¦ , π₯ = 0 , and π¦ = 3 is rotated about the π¦ -axis. Find the volume of the resulting solid.

Q2:

The region bounded by the curves π₯ = 2 β π¦ , π₯ = 0 , and π¦ = 8 is rotated about the π¦ -axis. Find the volume of the resulting solid.

Q3:

Find the volume of the solid generated by turning, through a complete revolution about the π¦ -axis, the region bounded by the curve 9 π₯ β π¦ = 0 and the lines π₯ = 0 , π¦ = β 9 , and π¦ = 0 .

Q4:

Find the volume of the solid generated by turning, through a complete revolution about the π¦ -axis, the region bounded by the curve 3 π₯ + 8 π¦ = 0 and the lines π₯ = 0 , π¦ = β 1 , and π¦ = 0 .

Q5:

Find the volume of the solid generated by turning the region bounded by the curve π¦ = 6 π₯ 2 , the π¦ -axis, and the lines π¦ = 3 and π¦ = 4 through a complete revolution about the π¦ -axis.

Q6:

Let π and π be constants. Find the volume of the solid of revolution produced on turning the region bounded by the curve β 2 π¦ π + π₯ π = 1 2 2 2 2 and the π₯ -axis about the π¦ -axis.

Q7:

Let π and π be constants. Find the volume of the solid of revolution produced on turning the region bounded by the curve β 7 π¦ π + π₯ π = 1 2 2 2 2 and the π₯ -axis about the π¦ -axis.

Q8:

Find the volume of the solid generated by revolving the region bounded by the curve π¦ = 8 π₯ and the straight lines π¦ = β 4 and π₯ = 0 a complete revolution about the π¦ -axis.

Q9:

Find the volume of the solid generated by revolving the region bounded by the curve π¦ = 6 π₯ and the straight lines π¦ = β 3 and π₯ = 0 a complete revolution about the π¦ -axis.

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