Lesson Worksheet: Volumes of Solids of Revolution Mathematics • Higher Education

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In this worksheet, we will practice finding the volume of a solid generated by revolving a region around either a horizontal or a vertical line using integration.

Q1:

Which of the following has the volume represented by the integration ?

Aa sphere whose radius length is 25 units
Ba sphere whose radius length is 5 units
Ca right circular cylinder whose height is 15 units and radius is 5 units
Da right circular cone whose height is 15 units and radius is 25 units
Ea right circular cylinder whose height is 5 units and radius is 15 units

Q2:

Consider the region bounded by the curves , , , and . Determine the volume of the solid of revolution created by rotating this region about the -axis.

A
B93
C
D
E186

Q3:

Find the volume of the solid generated by turning, through a complete revolution about the -axis, the region bounded by the curve and the lines , , and .

A3 cubic units
B cubic units
C cubic units
D27 cubic units

Q4:

Find the volume of the solid generated by rotating the region bounded by the curve and the -axis a complete revolution about the -axis.

A cubic units
B cubic units
C cubic units
D cubic units

Q5:

The region bounded by the curves , , and is rotated about the -axis. Find the volume of the resulting solid.

Q6:

Find the volume of the solid obtained by rotating the region bounded by the curve and the lines and about the -axis.

Q7:

Let and be constants. Find the volume of the solid of revolution produced on turning the region bounded by the curve and the -axis about the -axis.

Q8:

Find the volume of the solid obtained by rotating the region bounded by the curve and the line about the -axis.

Q9:

Find the volume of the solid obtained by rotating the region bounded by the curves and about the -axis.

Q10:

Consider the region between the curves and , for . Find the volume of the solid of revolution obtained by rotating this region about the -axis, giving your answer to two decimal places.

This lesson includes 56 additional questions and 217 additional question variations for subscribers.

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