Prisms © T Madas

W h a t i s a p r i s m? It can even have a hole in its cross section © T Madas

W h a t i s a p r i s m? It can even have a hole in its cross section © T Madas

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 © T Madas

Naming some Special Prisms Pentagonal Prism Cuboid (rectangular prism) Cylinder (circular prism) © T Madas

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 © T Madas

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 © T Madas

Volume of prisms © T Madas

© T Madas

1 Layer = 16 cubes Area = 16 cm2 Volume = 16 x 5 Volume = 5 x 16 © T Madas

1 Layer = 13 cubes Area = 13 cm2 Volume = 13 x 6 Volume = 6 x 13 © T Madas

Work out the volume of these prisms in cm3. © T Madas

Work out the volume of these prisms in cm3. © T Madas

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 © T Madas

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 © T Madas

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 © T Madas

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 © T Madas

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 © T Madas

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 © T Madas

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 © T Madas

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 © T Madas

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 © T Madas

The Volume of some Prisms Pentagonal Prism Cuboid Cylinder V = Ah V = Ah V = Ah V = lwh V = πr 2h © T Madas

© T Madas