Slice a solid. Meet the section.

SparkClass

Turn the solid, position a real mathematical plane, then extract the two-dimensional face inside.

CCSS 7.G.A.3 · Grade 7
Your Investigation
1Predict
→
2Cut
→
3Reveal
Live 3D Workbench
Drag to rotate
Interactive solid and cutting plane A rectangular prism intersected by a movable plane. Drag to rotate the three-dimensional view.
Rectangular Prism · Uncut
z points up
gold = cutting plane
01

A rectangle appears. The plane is parallel to the prism's base.

Same section, same color
3D SolidRectangular prism
+
Cutting Plane · n · p = hh 0.00 · θ 0° · φ 0°
→
2D Cross-SectionRectangle

Teacher notes — make the cut meaningful

Use the controls to focus attention on the plane before naming the result. The 3D cap and the flattened 2D section always share the same coral color.

1

Predict without a formula

Load a shape challenge. Ask which faces or curved surfaces the plane will meet, then have students choose a prediction before cutting.

2

Cut, separate, and rotate

Drag the 3D view during or after extraction. The exploded view separates the two pieces; rotate to inspect the congruent coral cut faces.

3

Compare across solids

Contrast horizontal sections of the prism, cylinder, and pyramid. Ask why the pyramid's square changes size while the prism's rectangle and cylinder's circle do not.

∑

Read the plane model

The plane is n · p = h, with tilt θ and turn φ. At θ = 0°, h is height z; at θ = 90°, h is the horizontal distance from the central axis. The offset is measured in units.

CCSS 7.G.A.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. This lab uses “trapezoid” to mean exactly one pair of parallel sides. Curved cylinder sections are rendered from dense samples of the exact ellipse-plus-cap constraints.