12-10 Surface Area of Pyramids and Cones

Transcription

1 Find the lateral and surface area of each figure. 1. Find the lateral and surface area of each figure m 2 ; 533 m in 2 ; 340 in in 2 ; in yd 2 ; 620 yd mm 2 ; 336 mm 2 4. The Luxor Hotel in Las Vegas, Nevada, is a square pyramid made from glass with base lengths of 646 feet and a slant height of feet. Find the surface area of the glass on the Luxor mm 2 ; mm 2 8. triangular pyramid: base side length 6 in., base area in 2, slant height 8 in. 72 in 2 ; 87.6 in 2 615,379.6 ft 2 9. Brianne is making a necklace using the bead shown. Find the approximate surface area of the silver bead mm 2 esolutions Manual - Powered by Cognero Page 1

2 10. The Transamerica Building in San Francisco is shaped like a square pyramid. It has a slant height of about 856 feet, and each side of its base is 145 feet. Find the lateral area of the building. 248,240 ft 2 Find the lateral and surface area of each figure. 11. Find the surface area of each figure. Round to the nearest tenth cm cm 2 ; cm ft 2 ; 91.1 ft in Adrienne is making costumes for the school play. She needs to make eight conical medieval hats. She wants each hat to have a slant height of 18 inches with a base circumference of 22 inches. How much material will she use to make the hats? Round to the nearest tenth. about in ft 2 ; ft cone: diameter 19 cm, slant height 30 cm cm 2 ; cm 2 esolutions Manual - Powered by Cognero Page 2

3 Draw the figure represented by each net. Then find the lateral and total surface area of each pyramid in 2 ; in cm 2 ; 160 cm A can of water repellant will seal a canvas that is 50 feet by 60 feet. Delsin wants to make a tent in the shape of a cone with a diameter of 30 feet. Find the slant height of the largest tent he can make with a floor that will use only one can of water repellant to seal the outside surface feet 22. Multiple Representations In this problem, you will examine surface areas of pyramids. a. Table Find the surface area of a square pyramid with a base side length of 1 and a slant height of 10. Then complete the table m 2 ; 174 m 2 b. Analyze What happens to the surface area if the base length and slant height are doubled, tripled, or multiplied by 4? c. Words Predict the surface area of a pyramid with the side length of 5 and slant height of 50. Then check your prediction. a. b. Sample answer: The original surface area is multiplied by the square of the scale factor. c. 525 square units esolutions Manual - Powered by Cognero Page 3

4 23. Identify Structure Draw a cone with a surface area that is between 100 and 150 square units. See students work. 24. Justify Conclusions Which has a greater surface area: a square pyramid with a base of x units and a slant height of l units or a cone with a diameter of x units and a slant height of l units? Explain your reasoning. The square pyramid; Sample answer: The surface area of the pyramid is x 2 + 2xl. If you use π 3.14, the surface area of the cone is 0.785x xl. For all positive values of x and l, the surface area of the pyramid is greater than the surface area of the cone. 25. Persevere with Problems The dimensions of the prism shown are increased by a scale factor and the total surface area of the new prism is 240,000 square meters. What was the scale factor used to create the new prism? Building on the Essential Question Explain how to find the surface area of a cone if you are given the diameter and the slant height of the cone. Sample answer: Determine the radius r, half the length of the diameter. Use πr 2 to calculate the area of the circular base, and πrl to find the lateral surface area of the cone. Add these to find the total surface area. 27. Find the surface area of a cone with a radius of 6 centimeters and slant height of 15 centimeters. A cm 2 B cm 2 C cm 2 D cm 2 C 28. Find the area of the ice cream cone covered by the wrapper. F 9.4 in 2 G 11.2 in 2 H 15.5 in 2 J 20.0 in 2 F 29. A square pyramid has a base with sides measuring 7 meters. If the surface area of the pyramid is 189 square meters, which of the following is the slant height of the pyramid? A 8 m B 10 m C 14 m D 16 m B esolutions Manual - Powered by Cognero Page 4

5 30. Short Response A square pyramid has a surface area of 39 square feet. After a dilation, the surface area is 351 square feet. What was the scale factor of the dilation? 3 For exercises 31 33, find the lateral and surface area of each three-dimensional figure. 31. cylinder: radius 6 inches, height 10 inches in 2 ; in cylinder: diameter 5.7 meters, height 2.3 meters 41.2 m 2 ; 92.2 m equilateral triangular prism: base height 10.4 feet, base length 12 feet, prism height 3 feet 120 ft 2 ; ft Find the volume of an ice cream cone that has a radius of 28 mm and a height of 117 mm. 96,057.3 mm Mrs. Morales used the parallelogram shown as a pattern for a paving stone for her sidewalk. If m 1 is 130, find m A skateboard with a regular price of $80 is on sale for 15% off. If Xavier buys the skateboard on sale, then pays 5% sales tax, what is his total bill? $71.40 Solve each proportion. 38. = = = = = = Find the discount for a $45 shirt that is on sale for 20% off. $9 esolutions Manual - Powered by Cognero Page 5

6 44. Find the mean and the mean absolute deviation of the set of points scored by a player in four games. 25, 11 esolutions Manual - Powered by Cognero Page 6