Students learn to measure three-dimensional solids — finding the volume (space inside) and surface area (skin outside) of prisms, cylinders, cones, spheres, and pyramids — and discover the elegant one-third relationships that connect them.
Students will be able to…
How much water fills a cone, how much paint covers a sphere, and why is a cone exactly one-third of a cylinder? Solid geometry has surprisingly elegant answers.
Project this and tap each solid. Have students record its volume and surface-area formulas and note the one-third patterns.
Tap any phase to open the teacher moves and student actions.
How much fills a cone — and how much paint covers it?
Teacher models.
Class uses the Solids Explorer.
Students compute.
One solid.
Aligned to the Common Core State Standards for Mathematics (High School: Geometry).
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Give an informal argument for the volume formulas.
Use geometric shapes and measures to model objects.
Identify shapes of cross-sections of solids.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students find the volume of a composite solid (like a cylinder topped with a cone) by adding the parts. A printable solids sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.