Multiple Choice Practice
 Geometric Relationships
Geometry Level
 Geometry Index | Regents Exam Prep Center

Also available in Hardcopy (.pdf):
Geometric Relationships
 

Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use your graphing calculator when working on these problems.
1.   The radius of a sphere is 5 feet.  Find the area of the great circle of this sphere.
       [1]                   [2]                   [3]                [4] 
 

 

2.  A cylinder and a cone each have a radius of 3 in. and a height of 8 in.  What is the ratio of
     the volume of the cone to the volume of the cylinder?

     [1]  Vcone : Vcylinder = 1 : 2
     [2]  Vcone : Vcylinder = 1 : 3
     [3]  Vcone : Vcylinder = 1 :
     [4]  Vcone : Vcylinder = 1 : 1
 

 

3.  Find the volume of a prism whose base is an equilateral triangle with a side of 4 and
     whose length is 6.


     [1] 24     [2]        [3]       [4]  48

 

4.  The surface area of a regular square pyramid is  where B is the area of the base,
     p is the perimeter of the base and s is the slant height.  If the base is a square with a side
    length of 10 and the slant height is 15, find the surface area of the pyramid.

     [1]  85                      [2]  220                    [3]    310              [4]  400
 

 

5.  Which of the following formulas will find the surface area of a cylinder with one open end
     and one closed end? 

     [1] 
     [2] 
     [3] 
     [4] 
 

 

 

6.  Which platonic solid will be created when the net shown at the right is
     assembled?

     [1]  tetrahedron

     [2]  cube 

     [3]  octahedron

     [4]  dodecahedron

 

7.  Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter.  How
     many cubic inches of  soda are contained in a full can?
      (Round answer to the nearest tenth of a cubic inch.)?

    [1]  12.0                   [2]  18.8                [3]  24.0               [4]  75.4
 

 

8.  Find the volume, to the nearest cubic inch, of a cone whose radius is 12 inches and whose
     height is 15 inches.

     [1]  2827                [2]  2262                [3]  565                [4]  188
 

 

9.  Top soil is sold by the cubic yard.  To the nearest cubic yard, how much top soil is needed
     to create a flower bed with soil 4 feet wide by 25 feet long by 6 inches deep?

     [1]  50                        [2]  27                       [3]  6                      [4]  2
 

 

10.  How many sides does a polygon have if the sum of its interior angles is 720°?

     [1]  5                       [2]  6                      [3]  7                   [4]  8
 

 

11.  Find the number of degrees in each interior angle of a dodecagon?

     [1]  135°                   [2]  144°               [3]  150°              [4]  cannot be
                                                                                                                     determined
 

 

12.  Find the sum of the exterior angles of a 15 sided polygon. 

     [1]  2340                    [2]  360                 [3]  156                 [4]  24
 

 

 

13.  If two planes are perpendicular to the same line,
     [1]  they are perpendicular.
      [2]  they are parallel.
     [3]  they intersect but are not perpendicular.
     [4]  none of the above.

 


 

14.  What is a polygon called if the sum of its interior angles equals 1440°?

     [1]  hexagon             [2]  octagon         [3]  decagon        [4]  dodecagon



 

15.  Each interior angle of a regular polygon measures 162°.  How many sides does the polygon
      have?

     [1] 20                   [2]  18               [3]  16            [4] cannot be determined
 

 

16.  When assembled, the net shown at the right will create a: 

     [1] cube.
     [2] cylinder.
     [3] cone.
     [4] prism.
 

 

17.  Find the volume of a hemisphere whose radius is 10 feet. 
       Round answer to the nearest cubic foot.
     [1] 419                [2] 1047               [3] 2094               [4] 4189
 

 

18.   How many sides in a cube?

     [1]  4                  [2]  6                   [3]  9                    [4]  12



 

19.  Find the measure of each exterior angle of a regular hexagon. 
   [1]  90°                 [2]  72°                [3]  60°                  [4]  45°
 

 

20.  Regarding the diagram at the right, which of the following statements is TRUE?
     [1] Planes l and q are parallel planes.
     [2] Planes l and q intersect in line .
     [3] Point P is in plane l.
     [4] None of the statements are true. 
 

Geometry Index | Regents Exam Prep Center