Surface Area of Prisms OCR Stage 8

A Prism Surface Area of Prism = Total of ALL individual surfaces Cylinder Cuboid Triangular Prism Trapezoid Prism Surface Area of Prism = Total of ALL individual surfaces

Area Formulae r h b Area Circle = π x r2 Area Rectangle = Base x height h b h b Area Trapezium = ½ x (a + b) x h a b h Area Triangle = ½ x Base x height

Surface Area Cuboid Area A = b x h C = 7.2 x 5.3 = 38.16cm2 B A Area B = b x h = 5.3 x 10.6 = 56.18cm2 7.2cm BUT there are 2 A’s, 2 B’s and 2 C’s 2 x A = 38.16 x 2 = 76.32cm2 Area C = b x h 2 x B = 56.18 x 2 = 112.36cm2 = 7.2 x 10.6 = 76.32cm2 2 x C = 76.32 x 2 = 152.64cm2 Total Surface Area = 341.32cm2

Surface Area of Cylinder Cross-sectional Area = π x r2 = π x 32 = 28.2743…..cm2 2 x Circles = 2 x 28.2743… = 56.5486… cm2 3cm 5cm 5 2πr Curved surface area = 5 x 2 x π x 3 = 94.2477….cm3 Total = 56.5486… + 94.2477.. = 154.796..cm2 = 154.8cm2

Surface Area - Trapezoid Prism Cross-sectional Area = ½ x(a + b) x h = ½ x (6.3 + 1.7) x 4.9 6.3cm C 4cm = 19.6cm2 B 4.9cm A 2 x A = 19.6 x 2 = 39.2cm2 8.2cm 2 x B = 8.2 x 4 x 2 = 65.6cm2 1.7cm D (the base) 1 x C = 8.2 x 6.3 = 51.66cm2 1 x D = 8.2 x 1.7 = 13.94cm2 Total Surface Area = 170.4cm2

Surface Area Triangular Prism Cross-sectional Area = ½ x b x h = ½ x 8.6 x 4.1 C [rear] 9.53cm = 17.63cm2 4.1cm B 4.9cm A DO NOT ROUND! 6.2cm 8.6cm D [the base] 2 x A = 17.63 x 2 = 35.26cm2 1 x B = 6.2 x 9.53 = 57.18cm2 1 x C = 4.1 x 6.2 = 25.42cm2 1 x D = 8.6 x 6.2 = 53.32cm2 Total Surface Area = 171.48cm2