Presentation on theme: "6-9 Surface and Area of Pyramids and Cones Warm Up Problem of the Day"— Presentation transcript:
1 6-9 Surface and Area of Pyramids and Cones Warm Up Problem of the Day Lesson PresentationPre-Algebra
2 6-9 Surface and Area of Pyramids and Cones Warm Up 2.48 m2 1186.9 cm2 Pre-Algebra6-9Surface and Area of Pyramids and ConesWarm Up1. A rectangular prism is 0.6 m by 0.4 m by 1.0 m. What is the surface area?2. A cylindrical can has a diameter of 14 cm and a height of 20 cm. What is the surface area to the nearest tenth? Use 3.14 for .2.48 m2cm2
3 Problem of the DaySandy is building a model of a pyramid with a hexagonal base. If she uses a toothpick for each edge, how many toothpicks will she need?12
4 Learn to find the surface area of pyramids and cones.
6 Regular PyramidThe slant height of a pyramid or cone is measured along its lateral surface.Right coneThe base of a regular pyramid is a regular polygon, and the lateral faces are all congruent.In a right cone, a line perpendicular to the base through the tip of the cone passes through the center of the base.
8 Additional Example 1: Finding Surface Area Find the surface area of each figure12A. S = B Pl= (2.4 • 2.4) (9.6)(3)12= ft2B. S = pr2 + prl= p(32) + p(3)(6)= 27p 84.8 cm2
9 Find the surface area of each figure. Try This: Example 1Find the surface area of each figure.12A. S = B Pl5 m= (3 • 3) (12)(5)12= 39 m23 m3 mB. S = pr2 + prl18 ft= p(72) + p(7)(18)7 ft= 175p ft2
10 Additional Example 2: Exploring the Effects of Changing Dimensions A cone has diameter 8 in. and slant height 3 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius.They would not have the same effect. Tripling the radius would increase the surface area more than tripling the slant height.
11 Triple the Slant Height Try This: Example 2A cone has diameter 9 in. and a slant height 2 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius.Original DimensionsTriple the Slant HeightTriple the RadiusS = pr2 + prlS = pr2 + pr(3l)S = p(3r)2 + p(3r)l= p(4.5)2 + p(4.5)(2)= p(4.5)2 + p(4.5)(6)= p(13.5)2 + p(13.5)(2)= 29.25p in2 91.8 in2= 47.25p in2 in2= p in2 in2They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.
12 Additional Example 3: Application The upper portion of an hourglass is approximately an inverted cone with the given dimensions. What is the lateral surface area of the upper portion of the hourglass?a2 + b2 = l2Pythagorean Theorem= l2l 27.9L = prlLateral surface area= p(10)(27.9) mm2
13 Try This: Example 3A road construction cone is almost a full cone. With the given dimensions, what is the lateral surface area of the cone?a2 + b2 = l2Pythagorean Theorem12 in.= l24 in.l 12.65L = prlLateral surface area= p(4)(12.65) in2
14 1. the triangular pyramid Lesson Quiz: Part 1Find the surface area of each figure to the nearest tenth. Use 3.14 for p.1. the triangular pyramid2. the cone6.2 m2175.8 in2
15 Insert Lesson Title Here Lesson Quiz: Part 23. Tell whether doubling the dimensions of a cone will double the surface area.It will more than double the surface area because you square the radius to find the area of the base.