its bases.
The bases are congruent polygons lying in parallel planes.
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Презентация, доклад на тему PRISMS Lateral Area and Total Area of a Prism (11th grade)
Содержание
- 1. PRISMS Lateral Area and Total Area of a Prism (11th grade)
- 2. Слайд 2
- 3. The faces of a prism that
- 4. The diagrams below show that a
- 5. Lateral Area and Total Area of a
- 6. Lateral Area and Total Area of a
- 7. home
- 8. Lateral Area and Total Area of a
- 9. Prisms have volume as well as area.
- 10. home
- 11. The Volume of a Right PrismThe same
- 12. Example 1A right trapezoidal prism is shown. Find the lateral area, total area,volume. home
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- 14. Example 2homeA right triangular prism is shown. The volume is 315. Find the total area.
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- 16. Example 3homeThe container shown has the shape
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- 18. Example 4A right prism has square bases
- 19. The Volume of an Oblique PrismThe
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- 21. The Volume of an Oblique PrismhomeVolume
- 22. Example 5The oblique square prism shown has
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- 24. Example 6
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- 26. NoteA diagonal of a right rectangular prism
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- 28. Example 7home
The faces of a prism that are not its bases are called lateral faces. The lateral faces of a prism are parallelograms. If they are rectangles, the prism is a right prism. Otherwise
Слайд 3 The faces of a prism that are not its bases
are called lateral faces.
The lateral faces of a prism are parallelograms.
If they are rectangles, the prism is a right prism. Otherwise the prism is an oblique prism.
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Слайд 5Lateral Area and Total Area of a Prism
The lateral area (L.A.)
of a prism is the sum of the areas of its lateral faces.
The total area (T.A.) is the sum of the areas of all its faces.
The total area (T.A.) is the sum of the areas of all its faces.
Слайд 6Lateral Area and Total Area of a Prism
L.A. = ah+bh+ch+dh+eh
= (a+b+c+d+e)h
= perimeter • h
= ph
= perimeter • h
= ph
The right pentagonal prism can be used to illustrate the development of the lateral area formula:
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Слайд 8Lateral Area and Total Area of a Prism
The Method applies to
any right prism.
The lateral area equals the perimeter of a base times the height of the prism. (L.A. = ph)
The lateral area equals the perimeter of a base times the height of the prism. (L.A. = ph)
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Слайд 9Prisms have volume as well as area. A rectangular solid with
square faces is a cube.
Since each edge of the blue cube shown is 1 unit long, the cube is said to have a volume of 1 cubic unit.
The larger rectangular solid has 3 layers of cubes, each layer containing (4•2) cubes. Hence its volume is (4•2)•3, or 24 cubic units.
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Volume = Base area x height
Слайд 11The Volume of a Right Prism
The same sort of reasoning is
used to find the volume of any right prism.
The volume of a right prism equals the area of a base times the height of the prism. (V = Bh)
The volume of a right prism equals the area of a base times the height of the prism. (V = Bh)
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Слайд 16Example 3
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The container shown has the shape of a rectangular solid.
When a rock is submerged, the water level rises 0.5 cm. Find the volume of the rock.
Слайд 18Example 4
A right prism has square bases with edges that are
three times as long as the lateral edges. The prism's total area is 750 m2. Find the volume.
Слайд 19The Volume of an
Oblique Prism
The volume of an oblique prism
equals the area of a base times the height of
the prism or right cross-section area times the length of the lateral edge.
Слайд 21The Volume of an
Oblique Prism
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Volume = Base Area x Altitude
= Right Cross-section Area x Length of lateral edge
Слайд 22Example 5
The oblique square prism shown has base edge 3. A
lateral edge that is 15 makes a 60° angle with the plane containing the base. Find the exact volume.
Слайд 26Note
A diagonal of a right rectangular prism joins two vertices not
in the same face. The length of the diagonals is
