Two solids, one object
Show on a big screenA round-bottomed toy, a tent, a capsule. None is a single basic solid.
- A toy: one smooth outline.
- A hidden seam runs round the middle.
- Above the seam sits a cone.
- Below the seam sits a dome.
Basic solids, joined
An object can be built from basic solids joined face to face. The join is a flat face where two solids meet.
- A round-bottomed toy is a cone on a hemisphere.
- A tent is a cone on a cylinder.
- A capsule is a cylinder with a hemisphere at each end.
A hemisphere is half of a sphere. Its curved part is also called a dome.
Here are the formulas for the basic solids. In them, r is the radius and h is the height. For a cone, l is the slant height. That is the length along its sloping side. In a cuboid, l, b and h are length, breadth, height.
| Solid | Curved surface | Total surface | Volume |
|---|---|---|---|
| Cylinder | 2πrh | 2πr(r + h) | πr²h |
| Cone | πrl | πr(l + r) | (1/3)πr²h |
| Sphere | 4πr² | 4πr² | (4/3)πr³ |
| Hemisphere | 2πr² | 3πr² | (2/3)πr³ |
| Cuboid | none | 2(lb + bh + hl) | lbh |
The book writes CSA for curved surface area. It writes TSA for total surface area. That is the curved surface plus the flat faces.
A cone mounted on a hemisphere has the cone on top. A cone surmounted by a hemisphere has the hemisphere on top.
Name each basic solid in the object. Find where the solids join. A join is a flat face where one solid meets another.
A test tube is a cylinder with a hemisphere at one end.
Name the solids in six objects.
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Try the lab to finish this lesson.