1. Prisms
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2. W h a t i s a p r i s m? It can even have a hole in its cross section
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3. W h a t i s a p r i s m? It can even have a hole in its cross section
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4. W h a t i s a p r i s m?
A prism is a 3-D shape that has the same cross section all the way through
cross sectional area
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5. Naming some Special Prisms
Pentagonal Prism
Cuboid
(rectangular prism)
Cylinder
(circular prism)
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6. Slanted Prism or Parallelepiped
S o m e o t h e r P r i s m s
Totally Irregular Prism
Slanted Prism or Parallelepiped
Triangular Prism
Polygonal Prism
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7. Last Notes on Prisms Volume of any Prism:
Bases h h
An Oblique or Slanted Prism
A Right Prism
Volume of any Prism:
Cross-Sectional Area (Base) x Height
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8. Volume of prisms
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10. 1 Layer = 16 cubes Area = 16 cm2 Volume = 16 x 5 Volume = 5 x 16
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11. 1 Layer = 13 cubes Area = 13 cm2 Volume = 13 x 6 Volume = 6 x 13
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12. Work out the volume of these prisms in cm3.
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13. Work out the volume of these prisms in cm3.
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14. EXAMPLE Method Total : Draw cross section B A
5 cm B
4 cm
10 cm
7 cm A
6 cm
12 cm
Find cross - sectional area
10 cm
A :
6 x 12 =
72 cm2
7 cm
B :
4 x 5 =
20 cm2
Total :
92 cm2
6 cm
Calculate Volume
12 cm
6 cm
Volume :
92 x 6 =
552 cm3
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15. EXAMPLE Method Total : Draw cross section B A
Find cross - sectional area
9 m
A :
6 x 8 =
48 m2
5 m
B :
3 x 3 =
9 m2
12 m
6 m
Total :
57 m2
8 m
Calculate Volume
Volume :
57 x 12 =
684 m3
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16. EXAMPLE Method Triangular prism Draw cross section
6 cm
4 cm
Find cross - sectional area
4 x 6 2
= 12 cm2
6 cm
10 cm
Calculate Volume
Volume :
12 x 10 =
120 cm3
4 cm
Triangular prism
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17. EXAMPLE Is there another way of calculating the volume of this prism?
Volume of the cuboid
4 x 10 x 6 =
240 cm3
Volume of the prism
6 cm
10 cm
240 ÷ 2 =
120 cm3
4 cm
Triangular prism
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18. EXAMPLE Method [ ] x 5 Trapezoidal prism Draw cross section
4 cm
5 cm
10 cm
4 cm
Find cross - sectional area
5 cm
8 cm
[ ] x 5 2
10 + 4
= 35 cm2
10 cm
Calculate Volume
Trapezoidal prism
Volume :
35 x 8 =
280 cm3
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19. EXAMPLE Method Total : Draw cross section A B C
Find cross - sectional area
1 m
A :
3 x 1 =
3 m2
1 m
B :
1 m
2 x 1 =
2 m2
C :
1 x 1 =
1 m2
1 m
1 m
Total :
6 m2
11 m
1 m
Calculate Volume
Volume :
6 x 11 =
66 m3
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20. EXAMPLE Method Total : Draw cross section A C B
Find cross - sectional area
A :
5 x 1 =
5 m2
5 m
1 m
B :
8 x 1 =
8 m2
C :
5 x 1 =
5 m2
6 m
12 m
Total :
18 m2
8 m
Calculate Volume
Volume :
18 x 12 =
216 m3
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21. The Volume of a Prism 150 cm3 50 cm3 348 cm3 540 cm3 140 cm3 144 cm3
Calculate the volumes of the following prisms.
Drawing the prisms is not needed, but you must show all your workings
All measurements are in cm 3
150 cm3 1 2 5 1 15
50 cm3
348 cm3 4 5 4 6 10 4 12 1 6 2 7 2
540 cm3 4
140 cm3 5 4 1
144 cm3 7 2 6 2 6 7 15 4 9 10 1 8
2480 cm3 2 6 5
9000 cm3 6 8 7 5 5 5 60 12 5 20 5 15
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22. V olume = Cross-sectional A rea x h eight
The volume of any prism
Cross sectional Area h
V olume = Cross-sectional A rea x h eight
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23. The Volume of some Prisms
Pentagonal Prism
Cuboid
Cylinder
V = Ah
V = Ah
V = Ah
V = lwh
V = πr 2h
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24. © T Madas