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**Objective: Be able to work out the volume of a prism.**

Volume of prisms Objective: Be able to work out the volume of a prism.

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**Volume of a prism You already know the volume of a cuboids height**

width length Volume = length x width x height

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Volume of a prism Instead, think of this as the area of the cross-section times the height height width length Area of cross-section = length x width Volume of prism = area of cross-section x height

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Volume of a prism What is the volume of a cuboids with dimensions 10 cm, 8 cm and 5 cm. 5 cm 8 cm 10 cm Area of cross-section = 10 cm x 8 cm = 80 cm2 Volume of prism = area of cross-section x height = 80 cm2 x 5 cm = 400 cm3

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Volume of a prism Volume of a cylinder is the area of the cross-section times the height Height h Radius r Area of cross-section = πr2 Volume of prism = area of cross-section x height Volume of cylinder = πr2h

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**Find the volume of a cylinder with radius 10 cm and height 20 cm**

Area of cross-section = πr2 = 3.14 x 102 = 3.14 x 100 = 314 cm2 Height 20cm Radius 10cm Volume of prism = area of cross-section x height Volume of cylinder = πr2h = 314 x 20 = 6,280 cm3

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**Find the volume of this prism**

Cross-section is a triangle Area of cross-section = ½ x 5 x 4 = 10 cm2 4 cm 5cm 14cm Volume of prism = area of cross-section x height length Volume of prism = 10 x 14 = 140 cm3

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**Find the volume of this prism**

Cross-section is a parallelogram Area of cross-section = 6 x 7 = 42 cm2 7 cm 6cm 15cm Volume of prism = area of cross-section x height length Volume of prism = 42 x 15 = 630 cm3

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