# Worksheet: Volumes by Slicing

In this worksheet, we will practice using integration to find the volume of a solid with a variable cross section.

Q1:

Use the slicing method to find the volume of the solid whose base is the region enclosed by and , and whose slices perpendicular to the -axis are right isosceles triangles with one side parallel to the -axis.

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Q2:

Use the slicing method to find the volume of the solid whose base is the region under the parabola in the first quadrant and whose cross-sectional slices are squares perpendicular to the -axis with one edge in the -plane.

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Q3:

Use the slicing method to find the volume of the solid of revolution bounded by the graphs of , , and and rotated about the .

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• E63

Q4:

Use the slicing method to find the volume of the solid whose base is the area between and and whose slices perpendicular to the are semicircles.

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Q5:

Use the slicing method to find the volume of the solid whose base is a triangle with vertices , , and and whose slices perpendicular to the -plane are semicircles.

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Q6:

Use the slicing method to find the volume of the solid whose base is the region inside the circle if cross sections taken perpendicular to the are squares.

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Q7:

Use the slicing method to find the volume of the solid whose base is the elliptical region with boundary curve and cross sections perpendicular to the are isosceles right triangles with the hypotenuse in the base.

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Q8:

Use the slicing method to find the volume of the solid whose base is the region under the parabola and above the and whose slices perpendicular to the are squares.

Q9:

Use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.

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Q10:

Use the slicing method to find the volume of the solid whose base is the region bounded by the lines , , and if the cross sections taken perpendicular to the are semicircles.

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Q11:

Using the slicing method, find the volume of the solid whose base is bounded by the curves and , between the first two intersections of the curves for , and whose perpendicular cross sections to the -plane are squares.

• A
• B2
• C1
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• E

Q12:

Find the volume of the solid of revolution generated by rotating the area bounded by and about the between the first two intersections of the curve and the line for .

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Q13:

Use the slicing method to find the volume of the solid whose base is bounded by the curves and and whose cross sections parallel to the -plane are semicircles.

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• E

Q14:

Find the volume of the solid of revolution generated by rotating the area bounded by and for about the .

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• E

Q15:

Find the volume of the solid of revolution generated by rotating the area bounded by and for about the .

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• E