Unit 8 Surface Area Volume Surface Area of

Unit 8 - Surface Area & Volume Surface Area of Pyramids and Cones

Lateral & Surface Area of a Pyramid l A Pyramid is a polyhedron with a base (can be any polygon) and other faces are triangles that meet at a common vertex. l Altitude – distance from top vertex straight down to the base (height) altitude (height)

Lateral & Surface Area of a Pyramid l A Pyramid is a polyhedron with a base (can be any polygon) and other faces are triangles that meet at a common vertex. l Slant height – distance from top vertex to bottom along one of the slanted sides slant height = l

Lateral & Surface Area of a Pyramid Draw a possible net for the pyramid.

Lateral Area of Pyramid l Lateral Area is the area of the lateral faces. On a pyramid, the lateral faces are 4 triangles. L. A. = 4 (area of the triangles) L. A. = 4 ( ½ b l ) A = ½ (base of )(height of ) Use l for height of triangle l L. A. = ½ p l b slant height = l Perimeter of Pyramid Base = 4 b b

Lateral & Surface Area of a Pyramid Surface area of a pyramid equals Lateral Area + area of the base of the pyramid How does this relate to surface area of a prism?

Lateral & Surface Area of a Pyramid l Find the surface area of the square pyramid using a formula. perimeter of base = 4(7. 5) = 30 area of Base = (7. 5) = 56. 25

Lateral & Surface Area of a Pyramid l Find the surface area of the square pyramid using a formula. perimeter of base = 4 ∙ 4 = 16 area of Base = 4 ∙ 4 = 16

Lateral & Surface Area of a Pyramid l Find the slant height and then use it to find the surface area of the pyramid.

Lateral & Surface Area of a Pyramid l Find the slant height and then use it to find the surface area of the pyramid. perimeter of base = 8 ∙ 6 = 48 area of Base = ½∙a∙p =½ ∙ 4√ 3 ∙ 48 =166. 3

Surface Area of Pyramids and Cones l End presentation here…SA of cones next

Surface Area of Cones A Cone has a circular base and one curved surface that is pointed at the top like a pyramid. The Lateral Area of a cone equals ½ the circumference of base times slant height How does this relate to LA of a pyramid?

Surface Area of Cones The Surface Area of a cone equals Lateral Area plus the area of the base How does this relate to surface area of a pyramid?

Surface Area of Cones

Surface Area of Cones l Find the surface area of the cone.

Surface Area of Cones l Find the slant height then find the surface area of the cone in -form.

Surface Area of Cones l Find the slant height then find the surface area of the cone in decimal form (to the nearest tenth) 2. 5 m