Practice with Solids
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Answer the following questions dealing with 3-dimensional figures.
Answers use = 3.141592654, the full calculator entry on the TI-83+/84+,
and are rounded to the nearest tenth unless otherwise stated.

1.


This figure is a regular hexagonal prism.
Find its volume.

Choose:

18 cu. units
93.5 cu. units
280.5 cu. units
 467.7 cu. units

 

 

 

2.

The radius of this sphere is 4 feet.
Find the area of the great circle of this sphere to the nearest tenth.

Choose:

12.7 sq. ft.
50.2 sq. ft.
 50.3 sq. ft.  
804.2 sq. ft.

 

 

3.

Find the volume of this right circular cone to the nearest cubic foot.

Choose:

110
80
 64  
47

 

 

4.

At the age of 81, Mr. Luke Roberts decided to start collecting string.  He has a spherical ball of string three feet in diameter.  On the assumption that one cubic inch of string weighs 0.03 pounds and the ball was solid string, how much does the ball weigh to the nearest tenth of a pound?

Choose:

73.0 lbs 
583.2 lbs
732.9 lbs 
2442.9 lbs 

 


 

5.

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

  

Choose:

Vcone : Vcylinder = 1 : 2
Vcone : Vcylinder = 1 : 3
 Vcone : Vcylinder = 1 :
Vcone : Vcylinder = 1 : 1

 
 

 

 

6.

The figure to the left is a cube.
Find the number of degrees in angle BEG.

Choose:

45°   
60° 
90° 

 

 

7.

Choose:

True
False 

If this 2-dimensional net is assembled, it will form the 3-dimensional figure shown at the right.

 

 

8.

This figure represents a slab of cheese.  It is in the form of a right triangular prism.  Find the least amount of wrapping needed to cover the cheese on all sides.

Choose:

18 sq. in.
24 sq. in.
 36 sq. in.  
48 sq. in.

 

 

9.

When you blow up a balloon it forms a sphere because it is trying to hold as much air as possible with as small a surface as possible.

How much air, to the nearest tenth of a cubic inch, is being held by a spherical balloon with a diameter of 12 inches?

Choose:

150.8 cu.in.
 226.2 cu.in.
904.8 cu.in. 
7238.2 cu.in.

 

 

10.

A regular pyramid is shown at the left.  Find the volume of the pyramid to the nearest cubic unit.

Choose:

800 
267
80
 27 

 

 

11.

Find the volume in
cubic feet.

Choose:
 

1575
4050
5625
6225
 
 

 

 

12.

The lateral surface area of a right circular cone, LS, is represented by the equation , where r is the radius of the circular base and h is the height of the cone.  If the lateral surface area of an ice cream cone is 236.64 square centimeters and its radius is 4.75 centimeters, find its height, to the nearest hundredth of a centimeter.
               

Choose:
 

251.47 cm
 228.91 cm
 15.86 cm
15.13 cm
 
 

 


 

13.

 A cylinder and a sphere have the same radius and the same height.  What is the ratio of the volume of the cylinder to the volume of the sphere?

Choose:

Vcylinder : Vshere = 1 : 1
Vcylinder : Vsphere = 2 : 1
 Vcylinder : Vsphere = : 3
Vcylinder : Vsphere = 3 : 2

 
 

 


 

14.

At the MetroPlex movie theater, popcorn is served in a box.  At the CinemaPlex movie theater, popcorn is served in a cylindrical container.  At home, Mom serves popcorn in a bowl (hemisphere in shape).  Based upon the given dimensions, where are you getting the most popcorn?
(Disregard the thickness of the container.)
                   

Choose:

MetroPlex
CinemaPlex
 Mom's Place
 

 


 

15.


This figure is a regular hexagonal prism.
Find its volume.

Choose:

41.6 cu. units
124.7 cu. units
 128.4 cu. units  
203.6 cu. units

 

 

16.

 In the chart below, the dimensions of a cylinder and a cone are doubled and tripled.  Find the volume of all three cylinders and all three cones.  When finished, state a hypothesis as to what happens to the volume of solids when the sides are doubled and tripled.

Cylinder: r = 4; h = 7 Doubled:  r = 8; h = 14 Tripled: r = 12; h = 21
Cone: r = 4; h = 7 Doubled: r = 8, h = 14 Tripled: r = 12; h = 21