Classwork Volumes by slicing warm up Name:

Give a formula for the area of the plane region in terms of the single variable m.

1. A square with sides of length m / 2. A square with diagonals of length m
3. A semicircle of radius m / 4. A semicircle of diameter m
5. An equilateral triangle with sides of length m / 6. An isosceles right triangle with legs of length m
7. An isosceles right triangle with hypotenuse of length m / 8. An isosceles triangle with two sides of
length 2m and one side of length m
9. A triangle with sides 3m, 4m, and 5m / 10. A regular hexagon of length m


VOLUMES OF CROSS-SECTIONS HOMEWORK #______Name:

For each solid, set up the integral, then use your calculator to find the volume.

1. The base of a solid is the region in the x-y plane bounded by the curves Cross-sections perpendicular to the x-axis are:
A. squares with one side in the base of the solid / B. equilateral triangles with one side in the base of the solid / C. isosceles right triangles with the hypotenuse in the base of the solid
2. The solid lies between planes perpendicular to the x-axis at x=-1 and x=1. The cross sections perpendicular to the x-axis between these planes run from the semicircle to the semicircle .
A. isosceles right triangles with one leg in the base of the solid and the right angle vertex on the curve / B. semicircles with the diameter in the base of the solid
3. The base of a solid is the region in the x-y plane bounded by the curves Cross-sections perpendicular to the x-axis are:
A. squares with one side in the base of the solid / B. semicircles with the diameter in the base of the solid

VOLUMES OF CROSS-SECTIONS HOMEWORK #______Name:

For each solid, set up the integral, then use your calculator to find the volume.

1. The base of a solid is the region in the x-y plane bounded by the curves Cross-sections perpendicular to the x-axis are:
A. squares with one side in the base of the solid / B. equilateral triangles with one side in the base of the solid / C. isosceles right triangles with the hypotenuse in the base of the solid
2. The solid lies between planes perpendicular to the x-axis at x=-1 and x=1. The cross sections perpendicular to the x-axis between these planes run from the semicircle to the semicircle .
A. isosceles right triangles with one leg in the base of the solid and the right angle vertex on the curve / B. semicircles with the diameter in the base of the solid
3. The base of a solid is the region in the x-y plane bounded by the curves Cross-sections perpendicular to the x-axis are:
A. squares with one side in the base of the solid / B. semicircles with the diameter in the base of the solid