3.5b: surface area of pyramids and cones gse’s primary m(g&m)–10–6 solves problems...

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3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three Secondary M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem)

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Page 1: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

3.5b: Surface Area of Pyramids and Cones

GSE’s

Primary

M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three

Secondary

M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem)

Page 2: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Pyramid: Lateral faces are triangles that share a common vertex.

(l)Slant Height: height of a lateral face

Page 3: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Find the surface areaof the Regular Pyramid

Page 4: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Find the Lateral Area of the regular pyramid

Page 5: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Cone: - base is a circle - has a vertex

Page 6: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Net View- What are the shapes?

Page 7: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Find the Surface Area

Page 8: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Find the Lateral area

Page 9: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

An entire grain silo needs to be painted with a rust proof paint. How many gallons of paint will need to be purchased ?

[1 gallon of paint = 300 sq feet]

10 ft

40 ft

10 ft

The circumference around the silo was approximated to be 63 ft

Page 10: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

Describe the shapes

Page 11: 3.5b: Surface Area of Pyramids and Cones GSE’s Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures

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