Pull a base. Build a prism.

SparkClass

Extrude one polygon through space, then slice it to see why V = B · H.

CCSS 7.G.B.6
Live Extrusion
0% extruded
Interactive right prism extrusion A right triangular base ready to be extruded through a prism height of 7 units.
Drag base ↕ to extrude · drag background to orbit
01

Start with one base. Drag the coral base upward, or press Play, to sweep it through H = 7.

Base Area · B12square units
×
Prism Height · H7units
=
Complete Volume84cubic units

Teacher notes — make the sweep visible

Start with the geometry, not the formula. The key idea is that every cross-section parallel to the base is congruent to that base.

1

Separate the two heights

Ask students to point to h_b inside the 2D base, then to H along the extrusion direction. Change one at a time. Which one changes B? Which one changes only how far the base travels?

2

Watch a copy become a solid

Reset to 0%, then drag the base or play the extrusion. The dashed coral polygon is the original base; the moving polygon is congruent to it. At 100%, all lateral edges are perpendicular to the base, so the result is a right prism.

3

Slice without changing the total

At 100%, open Layers / slices. Each slice has thickness Δh = H ÷ n and volume BΔh. Summing n slices gives n · B · (H/n) = B · H. Separating slices adds visual gaps, not mathematical volume.

?

Questions and common snags

Why does a triangular base need the factor ½? Why does a trapezoid use the sum of its two parallel sides? During a partial extrusion, use V_now = B · d, where d = pH; the ribbon always reports the complete target prism.

CCSS 7.G.B.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects. This lab targets the volume relationship for right triangular and trapezoidal prisms.

Access: Every action has a slider or button alternative. With reduced motion enabled, Play completes the extrusion immediately.