Quick Answer: Cylinder Cut in 8 parts Wooden is a wooden cylinder divided into eight pieces that fit back together, used to show where the volume formula of a cylinder, V = πr²h, comes from. Students rearrange the cylinder cut in 8 parts into a shape close to a cuboid and compare the two volumes.
From Round Solid to Near-Cuboid
In the usual form of this model the cylinder is cut along its axis into eight equal wedges, each with a sector-shaped cross-section. Laid side by side with the curved faces pointing alternately up and down, the wedges form a solid that looks like a cuboid with slightly wavy long sides. Its height is still the height h of the cylinder, its width is roughly the radius r, and its length is about half the circumference, which is πr.
Multiplying those three measurements gives πr × r × h, or πr²h. Students can check this with a ruler: measure the radius and height of the assembled cylinder, calculate πr²h, then rearrange the pieces, measure the length, width and height of the new shape and compare the two answers. The small difference comes from the curved edges, and that difference is where the lesson deepens. If the cylinder were cut into sixteen or thirty-two pieces, the edges would be flatter and the rearranged solid closer to a true cuboid.
The same reasoning connects to the familiar rule that the volume of any prism is its base area multiplied by its height. The base of a cylinder is a circle of area πr², and multiplying by the height gives the formula again. Seeing both routes arrive at one answer makes the formula feel earned rather than memorised.
Specifications
| Material | Wood, as named in the listing |
| Number of parts | 8 |
| Shape of each part (usual design) | Wedge with a 45° sector cross-section |
| Formula taught | Volume of a cylinder, V = πr²h |
| Diameter and height | Confirm at enquiry |
Applications
- Deriving V = πr²h by rearranging the eight parts into a near-cuboid
- Comparing a calculated volume with measurements of the rearranged shape
- Discussing why more, thinner parts would give a closer fit to a cuboid
- Showing one eighth, one quarter and one half of a solid using the parts
Care & Handling
- Wipe the wooden cylinder with a dry or barely damp cloth; soaking can swell the wood so the parts no longer fit.
- Store the eight parts assembled as a cylinder so none go missing between lessons.
- Handle the thin edges of each wedge gently, as a chipped edge spoils the fit.
Why Choose LabEquip
Middle and secondary maths teachers covering mensuration are the usual buyers, often alongside the Circle Kit that uses the same sector idea for the area of a circle. Both are listed in LabEquip’s Mathematics School Lab Products; send quantities through the contact page.
Frequently Asked Questions
How does rearranging the eight parts give the volume formula?
The parts are placed side by side, alternating their curved faces up and down, to make a shape close to a cuboid. Its length is about half the circumference, πr, its width is about the radius, r, and its height is the cylinder’s height, h. Multiplying gives πr²h.
Why is the rearranged shape not a perfect cuboid?
The long sides are made of curved arcs, so they are slightly wavy. With eight parts the curves are easy to see. The more parts a cylinder is cut into, the flatter those edges become, which is why the formula is exact even though the model is an approximation.
What angle does each part make at the centre?
If the eight parts are equal, each takes one eighth of a full turn at the centre of the circular face, which is 45 degrees. Students can check this with a protractor on the end face of one wedge.
How is this model connected to the area of a circle?
Rearranging sectors of a circle into a near-rectangle shows that the area of a circle is πr². The cylinder model adds height to the same idea, so its volume is that circular area multiplied by the height.
Can the parts be used to teach fractions of a solid?
Yes. One part is one eighth of the cylinder, two parts make one quarter and four parts make one half. Students can see that the half-cylinder has half the volume of the whole.
At what level is the model used?
It suits middle-school classes meeting the cylinder volume formula for the first time, and it is a useful revision aid for older students who know the formula but not why it works.
Last Updated: September 2026
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