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Mathematics
9th -
12thgrade
Geometry U11 L7/8 Cross Sections and Solids of Revolution
23 questions
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- 1. Multiple ChoiceDescribe the cross section.circleovalsemi-circletrapezoid
- 2. Multiple ChoiceDescribe the cross section.trianglerectangleovaltrapezoid
- 3. Multiple Choice
What is the area of the cross-section if the diameter of the base is 6 feet and the height of the cylinder is 8 feet.
24 ft2
48 ft2
8 ft2
4 ft2
- 4. Multiple Choice
Select the 2D object that can be rotated to form the 3D object shown.
- 5. Multiple Choice
What 3-D solid is formed when this rectangle is rotated about the vertical line?
Right, rectangular prism
Right, circular cylinder
Right, oval cylinder
Right, square prism
- 6. Multiple Choice
Which 2-D shape could be revolved about the vertical line to create the 3-D solid?
- 7. Multiple Choice
Which 3-D solid is created when the rectangle is rotated about the horizontal line?
- 8. Multiple Choice
A cylinder is cut parallel to the base. What is the shape of the cross-section formed?
Circle
Rectangle
Triangle
Trapezoid
- 9. Multiple Choice
A cone is cut by a plane that is perpendicular to its base. Which of the following could be the shape of the cross-section formed?
Circle
Triangle
Rectangle
Trapezoid
- 10. Multiple Choice
A right hexagonal prism is shown below. A two-dimensional cross section that is perpendicular to the base is taken from the prism.
Which figure describes the two-dimensional cross section?
triangle
rectangle
pentagon
hexagon
- 11. Multiple Choice
Rotating this circle around the diameter creates a ____________.
pyramid
sphere
cylinder
cone
- 12. Multiple Choice
The cross-section of a 3D figure is shaped like a circle. Which could NOT have been the 3D figure?
Sphere
Pyramid
Cylinder
Cone
- 13. Multiple Choice
Which shape is NOT a cross section of a cone?
Parabola
Ellipse
Circle
Square
- 14. Multiple Choice
The right triangle as shows is rotated about the in three dimensions. What is the 3-Dimensional solid resulting from the rotation?
cone
cylinder
pyramid
prism
- 15. Multiple Choice
Which of the shapes are possible cross-sections of a cube?
I and II
I, II and III
I, II and IV
I, II, III, and IV
- 16. Multiple ChoiceWhat is the volume of this rectangular prism?60 cubic centimeters15 cubic centimeters20 cubic centimeters6 cubic centimeters
- 17. Multiple Choice
Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.
True
False - the cross sectional areas are not relevant
False - only the slant height is relevant
False - even if they have the same cross sectional areas and heights, they cannot have the same volume.
- 18. Multiple Choice
Based on Cavalieri's Principle, will the two prisms have the same volume?
No, they will not be same. Although the heights are the same, the cross-sections are different shapes.
Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.
- 19. Multiple Choice
A right cylinder is cut perpendicular to its base. The shape of the cross section is a
circle
cylinder
rectangle
triangular prism
- 20. Multiple Choice
Select the 2D object that can be rotated to form the 3D object shown.
- 21. Multiple Choice
Both stacks of coins have the same number of the same kind of coins. Which has the larger volume - the coins stacked vertically or the coins pushed into a zigzag?
the coins stacked vertically
the coins pushed into a zigzag
they have the same volume
it cannot be determined without more information
- 22. Multiple Choice
The solids shown have the same height and the same Base area. Which has the larger volume?
the Right cylinder (on the left)
the Oblique cylinder (on the right)
they have the same volume
it cannot be determined without more information
- 23. Multiple Choice
Sheila believes that the two cylinders shown in the diagram below have equal volumes. Is Sheila correct or incorrect? Select ALL that apply.
Sheila is incorrect. The volumes of both cylinders are not equal.
Sheila is incorrect. One of the cylinders is tilted.
Sheila is correct. When two cylinders have the same base areas and the same height, their volumes must be the same.
Sheila is correct. Both cylinders radii and height are equal, so their volumes are the same.
Sheila is correct. Using Cavalieri’s Principle and the formula v=Bh or V=πr2h proves the volumes of the cylinders are equal.
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