Training module

GeoGebra for surface area and volume

GeoGebra para sa surface area at volume

Build and unfold 3D solids in GeoGebra so learners see where the surface area and volume formulas come from before they use them.

Time: 45 minutes
For: Grade 11 General Mathematics teachers (Term 1, Week 7)
Tools: GeoGebra

You will be able to

Construct prisms, pyramids, cylinders, cones and spheres in GeoGebra 3D.
Use the net tool to connect a solid's faces to its surface area formula.
Plan a lesson where learners compare volumes of combined solids such as a silo (cylinder plus cone).

Module

Getting GeoGebra

GeoGebra is free. The 3D Calculator runs in the browser (geogebra.org/3d) and as an Android or iOS app that works fully offline once installed, which makes it a good fit for schools with unreliable internet. Install the app on the shared devices before class.

Construct a prism and unfold it

SA_{\text{prism}} = 2B + Ph

V_{\text{prism}} = Bh

In the 3D view, draw a polygon on the xy-plane with the Polygon tool.
Choose Extrude to Prism and type a height, e.g. 5.
Select the Net tool and click the prism. Drag the slider from 0 to 1 to unfold it.
Ask: how many faces, which are congruent, and what is the area of each? Add up the faces to recover the formula.

Cylinders, cones and spheres

Use the Cylinder and Cone tools (click two points for the axis, then type a radius). Show the cylinder's net to justify the lateral area 2πrh: the rectangle's width is the circumference. For the sphere, fill a hemisphere with water in a video or use the GeoGebra 'volume' command and compare it to a cylinder of the same radius and height to motivate V = (4/3)πr³.

SA_{\text{cyl}} = 2\pi r^2 + 2\pi r h

V_{\text{cone}} = \tfrac13 \pi r^2 h

V_{\text{sphere}} = \tfrac43 \pi r^3

Combined solids from the community

Elaborate

Local objects make good combined-solid problems: a rice silo (cylinder plus cone), a water tank with a hemispherical top, a tent (triangular prism), an ice cream cone with a scoop. Learners measure or estimate dimensions, build the solid in GeoGebra, and compute the volume both by formula and with the Volume command to check.

Performance task idea

Extend

Design a container for a product sold in the local market (sachet, can, box) with a required volume. Learners justify their choice using surface area (material cost) and present the GeoGebra model. This matches the Term 1 performance standard on practical measurement solutions.

Try it

Build a cylinder of radius 3 and height 7, show its net, and compute its surface area by hand; compare with GeoGebra.
Prepare one combined-solid problem using an object in your community, with a photo and measurements.
Write the rubric criteria you will use for the container design task.