Paint the Pyramids Purple

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Presentation transcript:

Paint the Pyramids Purple 3D Trigonometry/Pythagoras

How much will it cost to paint the whole pyramid? The great pyramid at Giza in Egypt has a square base and four triangular faces. slanted edge How much will it cost to paint the whole pyramid? Your report should include Assumptions that you have made. Research findings Clear maths, diagrams and explanations. Conclusions/Improvements. Sommets 5 1 99 63 -17.00787 2 225 63 -17.00787 3 225 189 -17.00787 4 99 189 -17.00787 5 162 126 68.03149 Faces 5 1 4 4 3 2 1 2 3 1 2 5 3 3 2 3 5 4 3 3 4 5 5 3 4 1 5 BSommets 5

The top of the pyramid is directly above the centre of the base. The great pyramid at Giza in Egypt has a square base and four triangular faces. The base of the pyramid is of side 230 metres and the pyramid is 146 metres high. slanted edge The top of the pyramid is directly above the centre of the base. (i) Calculate the length of one of the slanted edges, correct to the nearest metre. Pythagoras’ theorem l 146 m Sommets 5 1 90 72 -17.00787 2 270 72 -17.00787 3 270 252 -17.00787 4 90 252 -17.00787 5 180 162 68.03149 Faces 5 1 4 4 3 2 1 2 3 1 2 5 3 3 2 3 5 4 3 3 4 5 5 3 4 1 5 BSommets 5 1 70.4549365234253 18.5097949350555 -90.9217083697797 2 245.53709547791 30.1395555679914 -131.05880197977 3 204.102094663231 100.878766349906 -291.305813700551 4 29.0199357087471 89.2490057169698 -251.168720090559 5 139.83922903418 137.698138286049 -157.341972681488 = 47754·76 l 2 146 l = 218·528.. 162·6 162·6 m = 219 m Sommets 5 1 99 63 -17.00787 2 225 63 -17.00787 3 225 189 -17.00787 4 99 189 -17.00787 5 162 126 68.03149 Faces 5 1 4 4 3 2 1 2 3 1 2 5 3 3 2 3 5 4 3 3 4 5 5 3 4 1 5 BSommets 5

(ii) Calculate, correct to two significant numbers, the total area of the four triangular faces of the pyramid (assuming they are smooth flat surfaces) slanted edge Pythagoras’ theorem 219 m h h 2 = 34736 = 186·375.. = 186·4 m 115 m 230 m Sommets 5 1 90 72 -17.00787 2 270 72 -17.00787 3 270 252 -17.00787 4 90 252 -17.00787 5 180 162 68.03149 Faces 5 1 4 4 3 2 1 2 3 1 2 5 3 3 2 3 5 4 3 3 4 5 5 3 4 1 5 BSommets 5 1 70.4549365234253 18.5097949350555 -90.9217083697797 2 245.53709547791 30.1395555679914 -131.05880197977 3 204.102094663231 100.878766349906 -291.305813700551 4 29.0199357087471 89.2490057169698 -251.168720090559 5 139.83922903418 137.698138286049 -157.341972681488 Area of triangle = base × height 1 2 = (230)(186·4) 1 2 = 21436 m2 2006 Paper 2 Q5 (b) Sommets 5 1 99 63 -17.00787 2 225 63 -17.00787 3 225 189 -17.00787 4 99 189 -17.00787 5 162 126 68.03149 Faces 5 1 4 4 3 2 1 2 3 1 2 5 3 3 2 3 5 4 3 3 4 5 5 3 4 1 5 BSommets 5

(ii) Calculate, correct to two significant numbers, the total area of the four triangular faces of the pyramid (assuming they are smooth flat surfaces) slanted edge Pythagoras’ theorem 219 m h h 2 = 34736 = 186·375.. = 186·4 m 115 m Sommets 5 1 90 72 -17.00787 2 270 72 -17.00787 3 270 252 -17.00787 4 90 252 -17.00787 5 180 162 68.03149 Faces 5 1 4 4 3 2 1 2 3 1 2 5 3 3 2 3 5 4 3 3 4 5 5 3 4 1 5 BSommets 5 1 70.4549365234253 18.5097949350555 -90.9217083697797 2 245.53709547791 30.1395555679914 -131.05880197977 3 204.102094663231 100.878766349906 -291.305813700551 4 29.0199357087471 89.2490057169698 -251.168720090559 5 139.83922903418 137.698138286049 -157.341972681488 Total area = 21436  4 = 85744 m2 = 86000 m2 2006 Paper 2 Q5 (b) Sommets 5 1 99 63 -17.00787 2 225 63 -17.00787 3 225 189 -17.00787 4 99 189 -17.00787 5 162 126 68.03149 Faces 5 1 4 4 3 2 1 2 3 1 2 5 3 3 2 3 5 4 3 3 4 5 5 3 4 1 5 BSommets 5