Rotating 2D Shapes to Create 3D Shapes

If an equilateral triangle is continuously rotated around one of its altitudes, which 3-dimensional object is generated?

• cone

• pyramid

• prism

• sphere

Circle O is centered at the origin. In the diagram below, a quarter of circle O is graphed. Which 3-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?

• cone

• sphere

• cylinder

• hemisphere

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

• Circle

• Triangle

• Rectangle

• Ellipse

A rectangle with dimensions of 8 inches by 16 inches is shown.

When the rectangle is rotated about the dotted line, the resulting figure is a ​ (a)   with a height of ​ (b)   and a radius of ​​ (c)  

• Cylinder

• Square Pyramid

• 8 inches

• 4 inches

• 16 inches

• 32 inches

Answer explanation

When a rectangle is rotated about a line, it forms a cylinder. The height of the cylinder is equal to the width of the rectangle (8 inches), and the radius is equal to the length of the rectangle (16 inches). Therefore, the resulting figure is a Cylinder with a height of 8 inches and a radius of 16 inches.

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

• A

• B

• C

• D

Identify the area of the cross section shown

• 7

• 16

• 12

• 8

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

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What 3D figure is formed by rotating a square around the y-axis?

• Sphere

• Cylinder

• Cone

• Pyramid