Practice Page
Directions: Read carefully and choose the best answer.

1.
A right circular cylinder and an oblique circular cylinder are given.

True or False? If the radii of both cylinders are equal, the volumes of the cylinders will be equal because they have the same height.

cav3
Choose:
True
False



2.
A right circular cylinder and a right rectangular prism are given.

True or False? Cavalieri's Principle does not apply to these solids because their bases are not the same shape.
cav5
Choose:
True
False



3.
cav9
  The three solids shown above have the same height and matching cross sectional areas parallel to the bases. Which of the solids have the same volume?
Choose:
 
 
A and C only.
A and B only.
 
B and C only.
A, B and C.



4.
A right circular cylinder, A, and an oblique circular cylinder, B, are shown at the right. Find the volume of cylinder B in cubic inches.
cav1
Choose:
 
 
110π in3
220π in3
440π in3
550π in3



5.
cav2
By Cavalieri's Principle, this right triangular prism and right rectangular prism have the same volume. If the center plane intersects the solids parallel to their bases, which of the following choices could be the base and height of the triangular cross section?
Choose:
 
 
h = 4; b = 12
h = 8; b = 12
 
h = 4; b = 8
h = 8; b = 14



6.
What is the volume of an oblique cylinder with a radius of 3 and a height of 9?
cav8

Choose:
 
27 units3
27π units3
 
81 units3
81π units3



7.
The right circular cylinder and the right rectangular prism have the same heights and the same base areas. A plane, parallel to the bases slices the two solids.
cav6
 
If the rectangular cross section has a base length of 16 inches and a width of 4π inches, what is the radius of the cylinder's cross section?
Choose:
 
 
32 in.
8π in.
8 in.
6π in.



8.
An oblique hexagonal prism has a base area of 68 square meters and a lateral (slant) side length of 10rad2 meters. The lateral side makes an angle of 45ยบ with the horizontal plane containing the base, as shown. What is the volume of the prism?
cav10
Choose:
 
 
34 m3
340 m3
100rad2m3
680 m3



9.
A right triangular prism and a right square prism are given. The base of the triangular prism is an isosceles right triangle with a hypotenuse of 6rad2.
cav7
  Both solids have a height of 10, and their bases have equal areas.
A plane slices both solids parallel to their bases. Find the length of the side of the square prism's cross section.
Choose:
 
 
4.5
3rad2
6
6rad2



10.
cavaliericoins cavaliericoin1
 

A series of coins are stacked to represent a right circular cylinder (on the left). The coins are then "slid" to represent a distorted cylinder (on the right). The same number of congruent coins was used in each stack.

Which of the following statements will be TRUE regarding these stacks of coins?
(Check all that apply, and hit SUBMIT!)

The volume of both stacks will be the same.

The area of a cross section parallel to the bases will not be equal due to the distorted nature of the second stack.

The height of the distorted stack will be slightly larger than that of the straight stack.
Cavalieri's Principle can be used in this situation to verify that the volumes of the stacks are equal.

        

 

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