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

1.
What 3-D solid is formed when this rectangle is rotated about the vertical line, as shown at the right?
revovle5
Choose:
 
right, rectangular prism
 
right, circular cylinder
 
right, oval cylinder
 
right, square prism



2.
Which 2-D shape could be revolved about the vertical line to create the 3-D solid shown at the right?

REVOLVE6
Choose:
 
revolve6c
revolve6b
revolve6a
revolve6d



3.
Which 3-D solid is created when the rectangle shown at the right is rotated about the horizontal line?
revolve7
Choose:
 
revolve7b
revolve7c
revolve7a
revolve7da



4.
Which 2-D shape could be revolved about the vertical line to create the 3-D vase shown at the right?
Assume the vase is open at the top and closed at the bottom.
greensurface

Choose:
 
greenvase3
 greenvase1 greenvase2 greenvase4



5.
A 3-D solid is formed by rotating the rectangle shown at the right about the vertical line. The dimensions of the rectangle are stated in inches. What is the volume of the solid formed by this rotation, in cubic inches?
REVOLVE9
 
Choose:
 
 
45 in3
45π in3
  90 in3 90π in3



6.
A rectangle and a right triangle, as shown at the right, are rotated about the vertical line. What is the volume of the solid formed by this rotation?
revolve10
Choose:
 
 
18 cubic units
 
24 + 16π cubic units
 
40π cubic units
 
52π cubic units



7.
The figure shown at the right was the result of a 2-D figure revolved about a line.
Which of the following figures, when rotated about the line, could NOT produce this 3-D shape?
revolvetrumpetw
Choose:
 
 
redparabolatrumpetw2
redparabolatrumpet4
  redparabolatrumpetw3 redparabolatrumpet6



8.
The 2-D figure at the right is to be revolved about the vertical line. Which of the following descriptions best describes the 3-D solid formed by the rotation?
nail
Choose:
 
Nail
 
Pencil
 
Water Glass
 
Gun



9.
The right triangle shown at the right is revolved about its hypotenuse. Find the volume of the solid formed by this rotation, in cubic units.
Hint: Find the altitude of the triangle drawn to the hypotenuse using the area of the triangle.
revolvepink
Choose:
 
76.8 π
72.6 π
40.8 π
19.1898 π



10.
Given: the 2-D figure at the right is a rectangle, and line a is perpendicular to line b.

 

Which of the following statements are true regarding this diagram?
(Check all that apply, and hit SUBMIT!)

 both
 
When the rectangle is revolved about line b, a solid cylinder is formed.

When the rectangle is revolved about line a, a rectangular prism is formed.

The volume of the solid formed when the rectangle is rotated about line a is 72π cubic units.

The volume of the solid formed when the rectangle is rotated about line a will equal the volume of the solid formed when the rectangle is rotated about line b.

        

 

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