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In this lesson, we will learn how to find the volume of the solid of revolution using the washer method around a horizontal line.

Q1:

Find the volume of the solid obtained by rotating the region bounded by the curve π¦ = π₯ ο© and the lines π¦ = 1 and π₯ = 2 about the line π¦ = β 1 .

Q2:

Determine the volume of the solid generated by rotating the region bounded by the curve π¦ = 7 π₯ 2 and the line π¦ = 7 π₯ a complete revolution about the π₯ -axis.

Q3:

Consider the region bounded by the curves π¦ = π₯ 3 and π¦ = π₯ , for π₯ β₯ 0 . Find the volume of the solid obtained by rotating this region about the π₯ -axis.

Q4:

Find the volume of the solid obtained by rotating the region bounded by the curve π¦ = 6 β π₯ ο¨ and the line π¦ = 5 about the π₯ -axis.

Q5:

Find the volume of the solid generated by turning the region bounded by the curve π¦ = π₯ + 2 2 , the π₯ -axis, and the two lines π₯ = β 2 and π₯ = 1 through a complete revolution about the π₯ -axis.

Q6:

Find the volume of the solid generated by rotating the region bounded by the curve π¦ = β π₯ + 2 π₯ 2 and the π₯ -axis a complete revolution about the π₯ -axis.

Q7:

Find the volume of the solid generated by turning the region bounded by the curves π¦ = 4 β π₯ , π¦ = β 8 , and π₯ = 5 a complete revolution about the π₯ -axis.

Q8:

Find the volume of the solid generated by turning the region bounded by the curves π¦ = 1 8 π₯ , π¦ = β 4 , π¦ = β 6 , and the π¦ -axis through a complete revolution about the π₯ -axis.

Q9:

Calculate the volume of a solid generated by rotating the region bounded by the curve π¦ = 4 5 π₯ and straight lines π₯ = 2 , π₯ = 8 , and π¦ = 0 a complete revolution about the π₯ -axis.

Q10:

Consider the region between the curves π¦ = 5 π₯ 2 and π₯ + π¦ = 2 2 2 , for π¦ β₯ 0 . Find the volume of the solid of revolution obtained by rotating this region about the π₯ -axis, giving your answer to two decimal places.

Q11:

Find the volume of the solid obtained by rotating the region bounded by the curves π¦ = 4 + π₯ s e c and π¦ = 6 about π¦ = 4 where π₯ β ο» β π 2 , π 2 ο . Give your answer to two decimal places.

Q12:

Consider the region bounded by the curve π¦ = 3 4 π₯ c o s 2 and the lines π¦ = 0 , π₯ = β π 8 , and π₯ = π 8 . Set up an integral for the volume of the solid obtained by rotating that region about π¦ = 4 .

Q13:

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve π¦ = π β π₯ 2 and the lines π¦ = 0 , π₯ = β 5 , and π₯ = 5 about π¦ = β 5 .

Q14:

Find the volume of the solid obtained by rotating the region bounded by the curves π¦ = π₯ s i n , π¦ = π₯ c o s , π₯ = π 6 , and π₯ = π 4 about π¦ = β 1 . Give your answer to two decimal places.

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