Geometry Surface Area of Pyramids and Cones
December 8, 2015 Goals Know what a pyramid is. Find the surface area of a pyramid. Know what a cone is. Find the surface area of a cone.
December 8, 2015 Pyramids
December 8, 2015 Pyramid Polyhedron with a polygon base. Lateral faces are triangles. Lateral faces meet at a common vertex. Regular pyramid: base is a regular polygon. (This is what we will discuss.)
December 8, 2015 Square Pyramid Vertex Altitude (h) Slant Height ( l )
December 8, 2015 Surface Area of a Pyramid The surface area is the sum of the area of the base and the area of the lateral faces. SA = B + LA
December 8, 2015 Surface Area of a Pyramid Unfold the pyramid: The surface area is the sum of the area of the base and the area of the lateral faces. S
December 8, 2015 Lateral Area Re-arrange the triangles.
December 8, 2015 Lateral Area Find the area of a triangle. S ? SSSS ? l l
December 8, 2015 Lateral Area Find the area of four triangles. S SSS l What is 4s? Perimeter!
December 8, 2015 Lateral Area of a Pyramid l
December 8, 2015 Surface Area of a Pyramid S l Just add the area of the base to the LA.
December 8, 2015 Example Find the LA & the SA of the square pyramid B = 12 2 = 144 P = 4(12) = 48 l = 16 LA
December 8, 2015 Example 2 Find the surface area of the square pyramid. 8 6 B = 8 2 = 64 P = 4(8) = 32 l = ?
December 8, 2015 Example 2 Finding the slant height. 8 6 ? 4 l
December 8, 2015 Example 2 Finding the SA
December 8, 2015 Your Turn Find the SA of the square pyramid
December 8, 2015 Finding the slant height
December 8, 2015 Finding the surface area
December 8, 2015 Example Find the lateral area
December 8, 2015 Cones Circular base No Lateral Faces SA = B + LA Can be right or oblique
December 8, 2015 Cone Surface Area Cut the cone from the vertex to the base. Then around the base. You get: Circular Base Circle Sector
December 8, 2015 Cone Surface Area A = r 2 Circular Base Circle Sector r l l The length of this arc is the circumference of the base. 2r2r
December 8, 2015 Sector Area Circle Sector l 2r2r This is the lateral area of a cone.
December 8, 2015 Cone Surface Area A = r 2 Circular Base Circle Sector r l l 2r2r A = r l SA = r 2 + rl
December 8, 2015 Cone Surface Area r l SA = r 2 + rl SA = r(r + l) LA = rl
December 8, 2015 Example Find the SA of the cone. 4 6 SA = r(r + l) SA = (4)(4 + 6) SA = 40 SA
December 8, 2015 Your Turn Find the SA of the cone SA = (5)(5 + 15) SA = (5)(20) SA = 100 SA
December 8, 2015 Example Find the SA of the cone. 8 3 l Finding l: 8.54
December 8, 2015 Example Find the SA of the cone. 8 3 Finding SA: SA = r(r + l) SA = (3)( ) SA = (3)(11.54) SA
December 8, 2015 Your Turn Find the surface area L 2 = L SA = π(12)( ) SA =
December 8, 2015 Now you can find the surface area and lateral area of cone or a pyramid!
December 8, 2015 Summary r l S l These should be on your formula sheet.
December 8, 2015 Practice Problems