Combination of Cube and Sphere (Transparent) for School Maths Lab

Quick Answer: Combination of Cube and Sphere (Transparent) for School Maths Lab is a see-through geometry model that presents a cube and a sphere together, so students can see how the two solids relate. The cube and sphere model supports mensuration lessons on volumes, surface areas and combinations of solids.

Why a Sphere and a Cube Belong Together

In the usual arrangement for this kind of model, the sphere sits inside the cube and touches all six faces, so the sphere’s diameter equals the cube’s edge. Transparent walls let students see that contact and measure it. If the edge is a, the cube’s volume is a³ and the sphere’s is (4/3)π(a/2)³ = πa³/6, so the sphere fills π/6 of the cube, a little over half.

The same comparison works for surface area: the cube has 6a² and the sphere 4π(a/2)² = πa², so the ratio is again π/6. Students are often surprised that both ratios match, and checking it with their own measurements of the model is good practice in substituting into formulas. The empty space between the two solids, a³ − πa³/6, gives a typical combination-of-solids question, such as how much packing material a ball needs in a cubical box.

A transparent model also helps with estimation before calculation. Asking the class whether the sphere takes up more or less than half the cube, before any formula is used, makes the final answer of about 52% memorable. The material, dimensions and exact arrangement of this model should be confirmed at the time of ordering.

Specifications

Applications

• Comparing the volume of a sphere with the cube that just contains it
• Comparing surface areas and finding the same π/6 ratio
• Word problems on combinations of solids and the space between them
• Estimating before calculating, then checking with measurements

Care & Handling

• Handle the model by its edges to avoid fingerprints and scratches on the clear faces.
• Clean with a soft cloth and mild soapy water; alcohol and solvent cleaners can cloud some clear plastics.
• Store it in a box or on a shelf where it cannot roll or be knocked off.

Why Choose LabEquip

Secondary maths teachers use this model in the surface area and volume unit, where many students struggle to picture one solid inside another. It is listed in LabEquip’s Mathematics School Lab Products range; send your requirement through the contact page.

Frequently Asked Questions

What fraction of the cube does the sphere fill?

When the sphere touches all six faces, its volume equals π/6 of the cube’s volume, about 0.52. So a little more than half of the cube is filled and a little less than half is empty space.

How do students calculate the empty space?

Subtract the sphere’s volume from the cube’s: a³ − πa³/6. For a cube of edge 10 cm that gives 1,000 − 523.6, or about 476 cm³ of space around the sphere.

Why is the surface area ratio the same as the volume ratio?

Both solids surround the same sphere of radius r, and for any solid whose faces all touch that sphere, the volume equals one third of r times the surface area. Since both volumes are r/3 times their surface areas, the two ratios must match.

Why is the model transparent?

So students can see where the sphere touches the cube and compare the diameter with the edge. An opaque model would hide the relationship the lesson depends on.

Which curriculum topic does the model support?

Surface areas and volumes, including problems on combinations of solids, usually studied in Classes 9 and 10. It also helps when the formula for the volume of a sphere is first introduced.

How can the model be used before formulas are taught?

Ask students to estimate what fraction of the cube the sphere occupies and record their guesses. Returning to those guesses after calculating about 52% shows how intuition about volume can mislead.

Last Updated: September 2026