Back to Exercise: Identify cross sections

Exercises: Identify Cross-Sections and Solids of Revolution

Grade 10·20 problems·~30 min·Common Core Math - HS Geometry·standard·hsg-gmd-b-4

Printable layout

Warm-Up

A cross-section is best described as:

The three-dimensional solid formed when a 2D shape is rotated about an axis

The two-dimensional shape visible when a plane cuts through a three-dimensional object

The outer curved surface of a cylinder or cone

A shape that can only be produced by cutting through the center of an object

A horizontal slice (parallel to the base) is taken through a cone. What shape is the cross-section?

Triangle

Rectangle

Circle

Ellipse

A solid of revolution is created by:

Stacking identical 2D cross-sections on top of each other

Rotating a two-dimensional shape about a line (axis)

Stretching a 2D shape in all three directions equally

Reflecting a 2D shape across a line to form a mirror image

Fluency Practice

$A cylinder with a vertical plane through its axis, highlighting the cut region and asking what shape the cross-section is$

A vertical plane passes through the axis of a cylinder (a plane containing the cylinder's central axis). What shape is the cross-section?

Circle

Ellipse

Rectangle

Triangle

A sphere of radius $R$ is sliced by a plane at a distance $d$ from the center, where $0 < d < R$ . What shape is the cross-section, and how does its size compare to a cross-section through the center?

Circle; larger than the great circle (center cross-section)

Ellipse; smaller than the great circle, because the off-center cut is tilted

Circle; smaller than the great circle (center cross-section)

Circle; the same size as the great circle, because all cross-sections of a sphere are equal

$A cylinder with an oblique cutting plane highlighting the cut region and asking what shape the cross-section is$

A cylinder is sliced by a plane that is tilted at an angle to the axis (oblique to the axis, not perpendicular and not parallel). What shape is the cross-section?

Circle

Ellipse

Parabola

Rectangle

A right triangle is rotated $360\degree$ about its vertical leg. Which solid is produced?

Cylinder

Sphere

Cone

Pyramid

A rectangle with width 3 cm and height 8 cm is rotated about its longer edge (height = 8 cm). Which solid is produced, and what are its dimensions?

A cylinder with radius 8 cm and height 3 cm

A cylinder with radius 3 cm and height 8 cm

A cylinder with radius 3 cm and height 3 cm

A cylinder with radius 8 cm and height 8 cm

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