Solids of revolution
Stick a cardboard rectangle to a pencil along one of its sides and spin it very fast: you will see a cylinder "appear". That is why the cylinder, the cone and the sphere are called solids of revolution.
How they are generated
Move the slider to see how the plane shape, as it rotates, "sweeps" through space and forms the solid:
| Shape that rotates | Axis of rotation | Solid that forms |
|---|---|---|
| Rectangle | one of its sides | Cylinder |
| Right-angled triangle | one of its legs | Cone |
| Semicircle | its diameter | Sphere |
Imagine sticking the following 2D shapes to a cocktail stick and spinning them quickly around it. Identify which solid of revolution is generated in each case: a) A…
Imagine sticking the following 2D shapes to a cocktail stick and spinning them quickly around it. Identify which solid of revolution is generated in each case:
- a) A rectangle rotating about one of its sides.
- b) A right-angled triangle rotating about one of its legs.
- c) A semicircle rotating about its diameter.
Draw in your notebook the solid of revolution generated by rotating the following 2D shape around the indicated axis. What is the name of the solid obtained? Describe…
Draw in your notebook the solid of revolution generated by rotating the following 2D shape around the indicated axis. What is the name of the solid obtained? Describe its main elements (bases, height and generatrix).
You can do it on paper and send a photo with your answer.
The net of the cylinder
If you cut a tin along a vertical line and "unroll" it, you get its flat net: two circles (the bases) and a rectangle (the lateral surface).
A tin of tennis balls is cylindrical in shape. The base has a diameter of $7$ cm and the height of the tin is $22$ cm. Calculate the curved surface area of the tin…
A tin of tennis balls is cylindrical in shape. The base has a diameter of $7$ cm and the height of the tin is $22$ cm. Calculate the curved surface area of the tin (excluding the caps).
The net of the cone
The net of the cone is a circular sector (a "slice of pizza") with radius equal to the slant height $g$, plus the circle of the base.
In the following drawing of a cone, identify the names of the parts labelled with the letters $r$, $h$ and $g$. Briefly explain what each of them represents.
In the following drawing of a cone, identify the names of the parts labelled with the letters $r$, $h$ and $g$. Briefly explain what each of them represents.
For a fancy-dress party, Lucía is making cone-shaped hats. If each hat has a slant height of $25\text{ cm}$ and the diameter of the base is $14\text{ cm}$, what will the…
For a fancy-dress party, Lucía is making cone-shaped hats. If each hat has a slant height of $25\text{ cm}$ and the diameter of the base is $14\text{ cm}$, what will the height of the hat be? Use Pythagoras' theorem to find it.
The sphere, a special case
You have a right cylinder and a right cone. The figure shows a horizontal cut (parallel to the base) with an orange dashed line and a vertical cut passing through the…
You have a right cylinder and a right cone. The figure shows a horizontal cut (parallel to the base) with an orange dashed line and a vertical cut passing through the centre of the bases (the axis of the solid) with a red dashed line.
- a) If we make the horizontal cut (parallel to the base) in a cylinder and in a cone, what plane geometric figure do we obtain as the cross-section in each one?
- b) Do we obtain the same figure in each solid if the cut is vertical and passes through the centre of the bases? State which figure results in the cylinder and which in the cone.