Deck 7: Extension B: Differential Equations

Question 1

Find the volume of a cap of a sphere with radius r = 100 and height h = 39

Answer 1

7857 π

Question 2

Find the volume of a pyramid with height and base an equilateral triangle with side a =

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

A)
B)
C)
D)
E) None

Answer 3

Question 4

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

Question 5

Find the volume of the solid obtained by rotating the region bounded by about the line

A)
B)
C)
D)
E)

Question 6

Find the volume of the frustum of a pyramid with square base of side square top of side and height

Question 7

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Question 8

The volume of a solid torus (the donut-shaped solid shown in the figure)with r = and R = is

Question 9

The base of S is the parabolic region Cross-sections perpendicular to the y axis are squares. Find the volume of S.

Question 10

Find the volume common to two spheres,each with radius r = if the center of each sphere lies on the surface of the other sphere.

Question 11

Find the volume of the solid obtained by rotating the region bounded by and about the line

Question 12

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

A)
B)
C)
D)
E)

Question 13

The base of S is a circular region with boundary curve Cross-sections perpendicular to the x axis are isosceles right triangles with hypotenuse in the base. Find the volume of S.