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In this lesson, we will learn how to calculate the volume of the solid generated from the revolution of a single variable function about the x- or y-axis.

Q1:

Determine, to two decimal places, the volume of the solid obtained by rotating the region bounded by the curve π¦ = 3 π π₯ and the lines π¦ = 0 , π₯ = β 1 , and π₯ = 1 about the π₯ -axis.

Q2:

Find the volume of the solid generated by revolving the region bounded by the curve π¦ = π₯ β 2 and straight lines π₯ = 1 and π¦ = 3 a complete revolution about the π₯ -axis.

Q3:

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve 9 π₯ + π¦ = 9 2 2 about π¦ = 5 .

Q4:

Which of the following has a volume of π οΈ 2 5 π₯ 1 5 0 d ?

Q5:

Determine, to two decimal places, the volume of the solid obtained by rotating the region bounded by the curve π¦ = π π₯ and the lines π¦ = 0 , π₯ = β 3 , and π₯ = 1 about the π₯ -axis.

Q6:

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve π₯ + 9 π¦ = 9 2 2 about π¦ = 4 .

Q7:

Find the volume of the solid generated by revolving the region bounded by the curve π¦ = π₯ β 1 and straight lines π₯ = 2 and π¦ = 3 a complete revolution about the π₯ -axis.

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