M3A 1.04-1.05 Cross Sections and Generating 3D Objects

​M3A 1.04-1.05: Cross Sections and Generating 3D Objects

By Sarah Reinhardt

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Multiple Choice

What shape will the horizontal cross-section of a cone be?

• Dome
• Circle
• Pyramid
• Triangle

Multiple Choice

What shape will the vertical cross -section of a cylinder be?

• Circle
• Triangle
• Rectangle
• Ellipse

Multiple Choice

What shape will the vertical cross-section of a cube be?

• Square
• Triangle
• Trapezoid
• Circle

Multiple Choice

What shape will the horizontal cross-section of a sphere be?

• Dome
• Circle
• Ellipse
• Rectangle

Multiple Choice

What shape does this cross section make?

• Rectangle
• Circle
• Triangle
• Square

Multiple Choice

What shape does this cross section make?

• Rectangle
• Circle
• Triangle
• Square

Multiple Choice

Describe the cross section.

• triangle

• rectangle

• trapezoid

• square

Multiple Choice

Describe the cross section.

• rectangle
• square
• oval
• circle

Multiple Choice

Describe the cross section.

• triangle
• rectangle
• oval
• trapezoid

Multiple Choice

What shape does this cross section make?

• circle
• Trapezoid
• Rectangle
• Parallelogram

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Multiple Choice

Which solid results from rotating the triangle using the axis of rotation shown?

• cone

• hexagonal pyramid

• triangular pyramid

• triangular prism

Multiple Choice

A rectangle and a horizontal line segment are shown. What is the resulting object when the rectangle is rotated around the horizontal line segment?

Multiple Choice

What 3D solid is produced by rotating the circle about line b?

Multiple Choice

The 2D shape is a right trapezoid. if you were to rotate the right trapezoid around segment AB, which of the following best describes the result?

• cylinder

• lamp shade

• cone

• hour glass

Multiple Choice

Which of the following would NOT be the result of rotating two triangles?

Multiple Choice

Which 3D shape will be formed if the semi-circle is rotated around axis E?

Multiple Choice

Circle O is centered at the origin.  In the diagram below, a quarter of circle O is graphed. Which three-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?

• cone

• sphere

• cylinder

• hemisphere

Multiple Choice

Select the 2D object that can be rotated to form the 3D object shown.

Multiple Choice

Identify the solid of revolution generated by revolving the region around the fixed line l.

• A

• B

• C

• D

Multiple Choice

Which of the following is NOT potential cross section formed when a cone is intersected by a plane?

Match

Match each 2D figure to the 3D solid that would be created by rotating it.

hollow cylinder

sphere

lampshade/ truncated cone

torus/ doughnut

cylinder

• hollow cylinder

• sphere

• lampshade/ truncated cone

• torus/ doughnut

• cylinder

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

Multiple Choice

The right prism with a triangular base shown below is cut by a plane perpendicular to its base. The two-dimensional shape of the cross section is always a…

• triangle

• rhombus

• pentagon

• rectangle

Multiple Choice

In the diagram below, a plane intersects a square pyramid parallel to its base. Which two-dimensional shape describes this cross section?

• circle

• square

• triangle

• pentagon

Drag and Drop

A rectangular prism is sliced by a plane parallel to its front face. What are the shape and area of the cross section?



Shape: ​​

Placeholder

Area of Cross Section: ​

Placeholder

cm³

Drag these tiles and drop them in the correct blank above

square

rectangle

diamond

triangle

55.2

253.92

10.58

21.16

Multiple Choice

Find the volume of the object generated by rotating the rectangle below about the vertical axis. Give your answers in terms of π.

• 250π cm³

• 500π cm³

• 62.5 cm³

• $$\frac{250}{3}\pi$$ cm³

Multiple Choice

The vertices of a triangle are (0, 0), (0, 7), and (10, 0). What is the volume, in cubic units, of the figure create by rotating the triangle about the y-axis?

• 700π cubic units

• 490π cubic units

• $$\frac{700\pi}{3}$$ cubic units

• $$\frac{490\pi}{3}$$ cubic units

Multiple Choice

The triangle below is rotated around the side labeled “5” to create a cone. What is the exact volume of this cone, in cubic units?

• 150π cubic units

• 240π cubic units

• 720π cubic units

• 300π cubic units

Fill in the Blanks

If the prism has a width of 4 cm, a height of 5 cm, and a volume of 160 cm³, what is the area of the cross-section shown, in cm²? Assume the cross section shown is parallel to the base of the prism.