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

1.
A right circular cone is shown at the right. The radius of the cone is 5 meters and the volume of the cone is 100π m3.
a) Find the height, h, of the cone.
bluecone
Choose:
 
4 m
8 m
 
10 m
12 m
 
blackbar

b)
Find the slant height, s, of the cone.
Choose:
 
12.5 m
12rad2 m
13 m
13rad3m



2.
Given a right square pyramid with base sides of 10 inches and all lateral edges of 10 inches.
a) Find the volume of the pyramid.
purppyramid
Choose:
 
purpvol2 m3
purpvol4m3
 
purpvol1m3
purpvol3 m3
 
blackbar

  b) A plane slices the pyramid, as shown, through its vertex perpendicular to the base, and coinciding with the diagonal of the base. Find the area of the cross section formed by this slice.
Choose:
 
25 in2
50 in2
75 in2
100 in2



3.
A right circular cone is shown at the right. A plane slices the cone parallel to the base 8 feet down from the vertex.

a)
Find the radius of the cross section.
yellowpyramid
Choose:
 
3 ft.
4 ft.
 
5 ft.
5.5 feet
blackbar
 
b)
Find the volume of the portion of the cone below the cross section.
Choose:
 
128over3ft3
34over3 ft3
432over3ft3
524over3 ft3



4.
A right, regular, hexagonal pyramid has a height of 12 units and a base side of 9 units. Find the volume of the pyramid to the nearest tenth of a cubic unit.
hexpyramid
Choose:
 
210.4 cubic units
 
621.2 cubic units
 
841.8 cubic units
 
2525.3 cubic units



5.
A right circular cone has a radius of 9 inches and a height of 12 inches. A slice perpendicular to the base passes through the vertex of the cone creating the cross section shown at the right. What is the perimeter of the cross section?
greencone3a
Choose:
 
 
48 in.
52 in.
 
60 in.
64 in.



6.
A right square pyramid has a height of 15 cm. and a slant height of 25 cm.
What is the volume of the pyramid?
Choose:
 
2400 square cm.
 
6000 square cm.
 
8000 square cm.
 
24000 square cm.

bluegraypyramid



7.
The lateral surface area of a right circular cone, LS, can be represented by the equation lsequation, where r is the radius of the circular base and h is the height of the cone. If the lateral surface area is 247.85 cubic cm, find the height to the nearest hundredth of a centimeter.

greebluecone
Choose:  
 
 
6.05 cm.
10.25 cm.
12.5 cm.
15.35 cm.



8.
The diagram at the right shows a right circular cylinder and a right circular cone with congruent bases and equal heights. If the cone section is removed from the cylinder, find the volume of the remaining section of the cylinder.

yellowbrowncylinder
Choose:
 
320 π cubic inches
 
640 π cubic inches
  960 π cubic inches
  1280 π cubic inches



9.
The ratio of similitude of two right rectangular pyramids is 3:4.
a) If the surface area of the smaller pyramid is 36 square inches, what is the surface area of the larger pyramid in square inches?
Choose:
 
42
48
64
100
 
b)
If the volume of the larger pyramid is 128 cubic feet, what is the volume of the smaller pyramid in cubic feet?
Choose:
 
27
54
72
96



10.
A plane slices a right circular cone parallel to its base at the midpoint of its height. The radius of the cone is 4 in. and its height is 12 in. If the cone is separated at the cross section, the bottom portion of the cone is called a frustum. frustum
  Which of the following statements are true regarding this diagram?
(Check all that apply, and hit SUBMIT!)
 

The volume of the cone is 192π cubic inches.

The volume of the frustum is 56π cubic inches.

The area of the cross section is 4π square inches.

The height of the frustum is 8 inches.

        

 

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