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Rotations on Grids -
Solids of Revolution Practice
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Practice Page
Directions: Read carefully and choose the best answer.

1.
If the triangle shown at the right is rotated about the y-axis, what 3-D solid will be formed?
grid1

Choose:
 
right, circular cylinder
 
right, circular cone
 
right, oval cylinder
 
right, oval cone



2.
What is the volume of the 3-D solid formed when the triangle shown at the right is rotated about the y-axis?
grid1

Choose:
 
16π cubic units
 
32π cubic units
 
48π cubic units
 
96π cubic units



3.
What is the volume of the 3-D solid formed when the rectangle shown at the right is rotated about the x-axis?
grid2

Choose:
 
 
30π cubic units
 
32π cubic units
 
34π cubic units
 
104π cubic units



4.
What is the volume of the 3-D solid formed when the two triangular shapes at the right are revolved about the x-axis?

Choose:
 
 
grid2a
 
24π cubic units
 
72π cubic units
 
88π cubic units



5.
What is the volume of the 3-D solid formed by rotating the triangle shown at the right about the y-axis?
 

Choose:
 
 
80π cubic units
 
grid4a
 
grid4b
 
160π cubic units



6.
A segment of the line f (x) = x, as shown at the right, is to be rotated about the x-axis. What is the volume of the carrying capacity of the 3-D figure created by this revolution, to the nearest cubic unit?

Choose:
 
 
17 cubic units
 
21 cubic units
 
42 cubic units
 
67 cubic units



7.
The grid at the right shows two semicircles enclosing a surface. When this figure is revolved about the y-axis, what will be the volume of the solid generated?
Choose:
 
 
grid61
 
grid62
 
grid63
 
grid64



8.
The 2-D figure at the right is a right triangle with a quarter circle removed. Find the volume of the solid formed when this shape is revolved about the y-axis?
Choose:
 
18π cubic units
 
grid72
 
grid71
 
43π cubic units



9.
The 2-D figure shown at the right is revolved about the y-axis. Find the volume of the solid formed by this rotation, in cubic units.
grid8

Choose:
 
 
50π cubic units
 
59π cubic units
 
68π cubic units
 
77π cubic units



10.
The 2-D figure shown at the right is a trapezoid. Find the volume of the solid formed when this figure is revolved about the y-axis.

Choose:
 
 
grid72
 
grid91
 
grid92
 
grid71

 

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