Slideshow 49, Mathematics Mr Richard Sasaki Room 307 Surface Area Slideshow 49, Mathematics Mr Richard Sasaki Room 307

Objectives Review how to find the area of various polygons Learn how to calculate the surface area of cuboids, triangular prisms and square- based pyramids Learn how to calculate the surface area of a cylinder

Answers 15𝑐 𝑚 2 49𝑐 𝑚 2 8𝑐 𝑚 2 108𝑐 𝑚 2 91𝑐 𝑚 2 70𝑐 𝑚 2 26𝑐 𝑚 2 204𝑐 𝑚 2 135𝑐 𝑚 2

Surface Area What is surface area? The total area of faces & surfaces on a 3D shape. Calculating surface area for cuboids and triangular prisms is easy as long as we know the dimensions of each face. 3 cm 2 cm 3 cm 3 cm 2 cm 2 cm 5 cm 5 cm

Surface Area - Cuboid 3 cm 15 cm2 6 cm2 10 cm2 6 cm2 2 cm 3 cm 15 cm2 All we do is add the total area of each face. We just simply add the numbers together. 10 + 15 + 10 + 15 + 6 + 6 = 10∙2+15∙2+6∙2 = 20+30+12 = 62𝑐 𝑚 2

Surface Area – Triangular Prism Visualising a net is always good! 3 cm 4 cm 5 cm 10 cm 3 cm 3 cm 4 cm 5 cm 4 cm 10 cm Surface Area: 10∙4 + 10∙3 + 10∙5 + 0.5∙4∙3 ∙ 2 = 40+ 30+ 50+ 12 = 132𝑐 𝑚 2

Answers 14𝑐 𝑚 2 216𝑐 𝑚 2 168𝑐 𝑚 2 156𝑐 𝑚 2 252𝑐 𝑚 2 270𝑐 𝑚 2

Square-Based Pyramids Let’s have a look at the square based pyramid. 𝑠 𝑠 𝑎 𝑎 𝑎 𝑎 This should be easy to calculate the surface area with too!

Square-Based Pyramids Example 7 𝑐𝑚 7 𝑐𝑚 4 𝑐𝑚 4 𝑐𝑚 4∙7∙ 1 2 ∙4 Surface area = 4 2 + =16+56 =72 𝑐 𝑚 2

Cylinders Let’s calculate the surface area of a cylinder with its radius and length. Example We know the cylinder is made of two and, if flattened a . circles rectangle 𝑙 =10𝑚 𝑟 =2𝑚 𝐶=2𝜋𝑟 4𝜋 𝑚 2𝑚 10𝑚

Cylinders S.A = 2∙𝜋 𝑟 2 + 2𝜋𝑟𝑙 𝐶=2𝜋𝑟 =2∙𝜋∙ 2 2 +2𝜋∙2∙10 4𝜋 𝑚 2𝑚 =8𝜋+40𝜋 10𝑚 =48𝜋 𝑚 2 On your test you won’t receive any formulae for surface area as the calculations are somewhat obvious but you are welcome to remember some if you need to!

Answers 40𝑐 𝑚 2 45 𝑚 2 161𝑚 𝑚 2 56𝑐 𝑚 2 105 𝑘𝑚 2 1035𝑘 𝑚 2

Answers 152𝜋 𝑐 𝑚 2 84 𝜋 𝑚 2 48𝜋 𝑐 𝑚 2 3.5𝜋 𝑚 2 480𝜋 𝑚 𝑚 2 16 𝜋 𝑘 𝑚 2