What it shows
A paper cone and a paper cylinder with the same base radius and the same height are filled with rice. Exactly three cones of rice fill the cylinder, showing that the volume of a cone is one third of pi r squared h.
The science
The volume of a cylinder is base area times height, pi r squared h. A cone with the same base and height tapers to a point, so it holds less, and calculus or a careful slicing argument shows it holds exactly one third. The rice makes this visible without any algebra: three level cone-fulls make one level cylinder-full. The same relation holds between a square pyramid and a cube-shaped box of the same base and height.
Materials
Cost: under Rs 50. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Chart paper or an old X-ray sheet
- A compass, ruler and protractor
- Tape
- About 1 kg of rice, sand or rajma
- A tray to catch spills
- A measuring cylinder or a kitchen scale to check
Safety
This project uses safe, everyday materials. Still, read the rules below with a parent before you start.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Draw a circle of radius 5 cm for the base and a rectangle 31.4 cm long and 12 cm high for the cylinder wall, since the circumference is 2 times pi times 5 which is about 31.4 cm.
Roll the rectangle into a tube, tape it, and tape the circle on as the base so it is sealed.
For the cone, draw a sector of radius 13 cm with angle 138 degrees, because the slant height is the square root of 5 squared plus 12 squared which is 13, and the arc must equal 31.4 cm.
Roll the sector into a cone and tape it. Check its height is 12 cm and its mouth just fits inside the cylinder mouth.
Fill the cone level with rice and pour it into the cylinder. Repeat and mark the level after each pour.
After three pours the cylinder should be level full. If it is short, the cone is probably not sealed at the tip; tape it.
Weigh one cone-full and one cylinder-full of rice on a kitchen scale and check the ratio is about 1 to 3.
Work out both volumes with the formula: cylinder 3.14 times 25 times 12 = 942 cubic cm, cone 314 cubic cm.
What you should see
Three level cone-fulls of rice fill the cylinder, and the weights give a ratio close to 1 to 3, matching cone volume 314 cubic cm and cylinder volume 942 cubic cm.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the volume of a cone?
One third of pi r squared h, where r is the base radius and h the vertical height.
2Why must the cone and cylinder have the same radius and height?
The one third rule compares a cone and cylinder on the same base with the same height; change either and the ratio changes.
3How did you find the sector angle for the cone?
The arc of the sector must equal the base circumference, so the angle is 360 times r divided by the slant height: 360 times 5 divided by 13, about 138 degrees.
4What is the slant height of this cone?
13 cm, from Pythagoras with 5 and 12.
Take it further
Make a hemisphere of the same radius from a ball cut in half and show it holds two cone-fulls, giving the sphere formula four thirds pi r cubed.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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