Here is another hands-on activity that uses modelling clay (earlier this used to be called ‘plasticine’). Carefully mold the clay into a solid cylinder and measure its radius and height. Then reshape the same portion of clay into identical cones, each having the same radius and the same height as the cylinder. You will find that you are able to make exactly three such cones.

Step-by-step solution

Idea: Reshaping clay never changes its volume. So if one cylinder’s worth of clay becomes exactly three equal cones, each cone is one-third of the cylinder.

1. Sample measurements: cylinder radius r = 2 cm, height h = 6 cm. Volume = π × 2² × 6 = 24π ≈ 75.4 cm³.½ mark
2. Reshape: three cones of radius 2 cm and height 6 cm use up all the clay. Volume is unchanged, so 3 × (volume of one cone) = 24π.1 mark
3. Each cone = 8π ≈ 25.1 cm³ = 13 × π × 2² × 6. In general, volume of a cone = 13πr²h.½ mark

Check: 13 × π × 4 × 6 = 8π ✓, and 3 × 8π = 24π, the cylinder ✓.

Answer to write in the exam

Common mistakes that cost marks

• Making cones of a different height or radius from the cylinder; then the count is not three.
• Thinking the clay’s volume changes when its shape changes.

How this can come in the exam

Try one yourself

A clay cylinder of radius 3 cm and height 10 cm is reshaped into cones of radius 3 cm and height 5 cm. How many cones are made?

More questions like this

• A right triangle ABC with sides 5 cm, 12 cm and 13 cm is rotated through 360° about the side with length 12 cm. Find the volume of the solid so obtained.
• Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
• Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.
• The height of a cone is 16 cm, and its base radius is 12 cm. Find the curved surface area and the total surface area of the cone.
• A cone has a height of 15 cm. If its volume is 1570 cm³, find the radius of the base.

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