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

1.
Given a right rectangular prism. If a cross section is made parallel to this base, which of the following statements regarding the area of the cross section and the area of the base of the prism is correct.
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Choose:
 
The area of the cross section is less than the area of the base.
 
The area of the cross section is greater than the area of the base.
  The area of the cross section is equal to the area of the base.
  The area of the cross section will be half the area of the base.



2.
A right square pyramid is sliced through its apex (vertex, top) perpendicular to its base, but parallel to a side of the base. The sides of the base have a measure of 12 inches. The perpendicular distance from the apex to the center of the base is 18 inches. What is the area of the cross section made by the slice, in square inches?
pyramidgreenn3slice
Choose:
 
30
54
 108 216



3.
Of the choices "square", "rectangle" and "triangle", which of the following are possible cross sections obtained when slicing a cube either parallel or perpendicular to its base?
crossguy2
Choose:
 
square only
 
square and rectangle only
 
square and triangle only
 
square, rectangle and triangle


4.
This right rectangular pyramid is sliced parallel to its base. Which of these two-dimensional shapes describes the cross section?
pyramidQ
Choose:
 
triangle
 
rectangle
  pentagon
  trapezoid



5.
A right triangular prism is sliced perpendicular to its base. Which of these two dimensional shapes best describes the cross section?
blueprism
Choose:
 
rectangle
 
triangle
  trapezoid
  pentagon



6.
Which of the following statements is FALSE regarding possible cross sections when slicing a right square pyramid?
Choose:
      A slice perpendicular to the base can yield a triangle.
      A slice perpendicular to the base can yield a square.
      A slice parallel to the base can yield a square.
      A slice perpendicular to the base can yield a trapezoid.



7.
Given a cube. A cross section is sliced diagonally through the center of the cube, as shown. Which of the following statements is true regarding the area of the cross section and the area of the cube's face?
crossFive
Choose:
 
The area of the cross section equals the area of the cube's face.
 
The area of the cross section is larger than the area of the cube's face.
 
The area of the cross section is smaller than the area of the cube's face.
 
There is insufficient data to determine the relationship between the area of the cross section and the area of the cube's face.



7.
A plane intersects a cube perpendicular to the base such that the cross sections are not parallel to a lateral side. Which of the following statements is NOT true regarding the two-dimensional cross sections that could be formed by the plane?
rrpcolored
Choose:
 
The cross sections are rectangles.
 
The cross sections are parallel to each other.
  The cross sections are of varying widths.
  The cross sections are of the same height.

 


8.
Given a right triangular prism as shown at the right. A cross section is made parallel to the bases. Which of the following statements is true regarding the area of the cross section and the area of the base?
crossFour
 
Choose:
 
The area of the cross section is less than the area of the base.
 
The area of the cross section is greater than the area of the base.
  The area of the cross section is equal to the area of the base.
  There is insufficient data to determine these area relationships.



9.
 A solid has a triangle as a cross section. Which of the following solids could NOT have a triangle as a cross section?
Allow for all possible orientations (angles) of the cross sections.
Choose:
 
Cube
 
Square pyramid
  Triangular prism
  Rectangular prism
  All of the above have triangular cross sections.

 

 

10.
 A cube and a right square pyramid are sitting on a flat surface. Which of the following statements are true?
(Check all that apply, and hit SUBMIT!)
crossTwo
 
It is possible to slice . . .
a triangular cross section from the cube.

a trapezoidal cross section from the pyramid.

a rectangular cross section (not a square) from the pyramid.

a hexagonal cross section from the cube.

a square cross section from the pyramid.

a hexagonal cross section from both the pyramid and the cube.

a square cross section from both the pyramid and the cube.

        

 

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