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3. Volume of a Prism Remember: Prisms are 3 dimensional shapes that have a constant cross-sectional area. Triangular-based prism Rectangular-based prism Pentagonal-based prism Hexagonal-based prism Octagonal-based prism Circular-based prism Cylinder Cuboid

4. Prisms The volume of any prism is simply its: cross-sectional area x length 9 m 2 100 cm 2 60 mm 2 2 m 9 cm 3 mm a b c V = 9 x 2 = 18 m 3 V = 100 x 9 = 900 cm 3 V = 60 x 3 = 180 mm 3 Diagrams Not to scale

5. Find the volume of the following prisms. 9 m 2 V = 9 x 5 = 45 m 3 Diagrams Not to scale 8 cm 2 7 mm 2 5 m 4 cm 10 mm 20 mm 2 10 mm 30 m 2 2½ m 40 cm 2 3 ¼ cm V = 8 x 4 = 32 cm 3 V = 7 x 10 = 70 mm 3 V = 20 x 10 = 200 mm 3 V = 30 x 2½ = 75 m 3 V = 40 x 3¼ = 130 cm 3 1 2 3 4 5 6

6. Find the volume of the following prisms. Diagrams Not to scale 4.3 m 2 8.2 cm 2 5.1 m 19.3 cm V = 4.3 x 5.1 = 21.93 m 3 V = 8.2 x 19.3 = 158.26 cm 3 V = 8.2 x 10.1 = 82.82 ft 3 V = 0.7 x 0.4 = 0.28 yd 3 8.2 ft 2 10.1 ft 0.7 yd 2 0.4 yd 1 2 3 4

7. Find the volume of the following prisms. Diagrams Not to scale In each of the following examples the cross-sectional ends have to be calculated. 4 m 2 m V = 4 x 1.5 x 2 = 12 m 3 1.5 m 8 cm 9 cm 4 cm 8 mm 7 mm 6 mm 5 mm 1 2 3 V = ½ (9 x 8) x 4 = 144 cm 3 V = ½ (8 + 6) x 7 x 5 = 245 mm 3 Remember: A = ½ base x height A = ½ the sum of the parallel sides x height

8. 5cm 8 cm 15 cm V = ½ x 20 x 16 x 4 = 640 cm 3 V =  x 8 2 x 10 = 3.142 x 64 x 10 = 2010cm 3 (nearest cm 3 ) 4 cm 10cm Remember: A =½ product of diagonals Remember: Area =  r 2 r 1 2

9. Worksheet 1 Triangular-based prism Pentagonal-based prism Hexagonal-based prism Octagonal-based prism Circular-based prism Volume of a Prism

10. Worksheet 2 a b c 1 2 3 4 5 6

11. Worksheet 3 1 2 3 4

12. Worksheet 4 1 2 3 4 5