1 A bh. 9 cm cm All Sides cm. 15 in

Transcription

1 .4 Surface Area A. Surface Area of Right Pyramid Polygon bae and Triangular face The um of the triangular face = lateral Area apex Height Slant height Bae. Regular Tetrahedron Bae i a equilateral triangle Lateral face are equilateral triangle 7.8 cm. Square Right Pyramid Bae i a quare Lateral face are triangle 9 cm A bh cm All Side cm 6 in. 5 in. All Side in Total S. A. A bh in Bae 55 5 in 85 in Formula on Formula Sheet for bae that are regular polygon: S. A. perimeter of bae bae area in

2 3. Rectangular Right Pyramid Bae i a rectangle Lateral face are triangle 6 ft. 8 ft. 0 ft. 0 ft. 6 ft. 8 ft. 6 ft. 6 ft. S 4 ft. S S S 5 ft. a b c a b c 8 Uing S Uing S A bh A bh triangle triangle SA.. area area Bae area = ft. See calculator key troke in picture... TI83+ TI84+

3 B. Cone r S. A. r r Lateral Area Circular Bae Eg. Find the Surface Area to the nearet quare metre. 0 m 4 m SA m Do not ue 3.4 for. Ue the button on calculator. (ee picture above) Eg. Given the lateral area of the cone i 0 cm and the diameter i 0 cm, find the height of the cone to the nearet tenth of a cm. 0 cm r = 5 cm h Lateral Area r cm 5 a b c 0 h 5 5 h h 5 h 3. cm 5 5 TI-84+ Example TI-84+ Example TI-83+ Example

4 Dicu the Idea. How do you determine the urface area of a right pyramid?. When you ee a picture of a right pyramid with a regular polygon bae, how do you identify it height and it lant height? 3. How i calculating the urface area of a right pyramid like calculating the urface area of a right cone? How i it different? Exercie A 4. Determine the lateral area of each right pyramid to the nearet quare unit. a) quare pyramid b) regular tetrahedron in. 6 in. 3.0 cm 5. Determine the urface area of each right pyramid in quetion 4, to the nearet quare unit. 6. Determine the lateral area of each right cone to the nearet quare unit. a) b) 4 in. 8 in. 5 cm.3 cm 35 cm 7. Determine the urface area of each right cone in quetion 6, to the nearet quare unit. 8. Calculate the urface area of each object to the nearet quare unit. a) right quare pyramid b) right cone B 9. The lant height of a right quare pyramid i 73 ft. and the ide length of the bae i 48 ft. a) Sketch the pyramid. b) Determine it lateral area to the nearet quare foot. 0. The Great Pyramid at Giza ha a quare bae with ide length 755 ft. and an original height of 48 ft. Determine it original urface area to the nearet quare foot.. Aiden built a cone-haped volcano for a chool cience project. The volcano ha a bae diameter of 3 cm and a lant height of 45 cm. a) What i the lateral area of the volcano to the nearet tenth of a quare centimetre? b) The paint for the volcano urface cot $.99/jar, and one jar of paint cover 400 cm. How much will the paint cot?. A road pylon approximate a right cone with perpendicular height 53 cm and bae diameter 8 cm. The lateral urface of the pylon i to be painted with reflective paint. What i the area that will be painted? Anwer to the nearet quare centimetre. 3. Determine the urface area of each right rectangular pyramid to the nearet quare unit. a) b) 4 cm 5 yd. 8.7 m 9.0 m 0 ft. 4 cm 8 yd. 5.4 m.8 m 5 ft. 8 ft. 34 Chapter : Meaurement

5 4. The Royal Sakatchewan Mueum in Regina ha a tipi in it Firt Nation Gallery. The tipi approximate a cone with a bae diameter of 3.9 m and a height of 4.6 m. A Cree woman from Chitek Lake tanned, prepared, and ewed 5 bion hide to make the cover. To the nearet tenth of a quare metre, what area did each bion hide cover? What aumption did you make? 5. A farmer unloaded grain onto a tarp on the ground. The grain formed a cone-haped pile that had a diameter of ft. and a height of 8 ft. Determine the urface area of the expoed grain to the nearet quare foot. 6. For each object, it urface area, SA, and ome dimenion are given. Calculate the dimenion indicated by the variable to the nearet tenth of a unit. a) right cone b) right quare pyramid 48 mm SA 70 mm 7. A toy block manufacturer need to cover it wooden block with a non-toxic paint. One block i a right quare pyramid with a bae length of in. and a lant height of 3 in. A econd block i a right cone that ha a lant height of 3 in. and a bae radiu of in. A third block i a right rectangular prim with bae dimenion in. by in. and a height of 3 in. a) When the block ret on their bae, which block i tallet? How do you know? b) Which block require the mot paint? 3.5 m SA 65.5 m 8. The Louvre art mueum in Pari, France, ha a gla quare pyramid at it entrance. The ide length of the bae of the right pyramid i 35.0 m and it height i 0.6 m. The Muttart Conervatory in Edmonton, Alberta, ha four right quare pyramid alo with gla face. One of the larget pyramid ha a bae ide length of 5.7 m and a height of 4.0 m. C Which pyramid require more gla to encloe it pace? 9. Determine the urface area of each right pyramid to the nearet tenth of a quare unit. a) a right pyramid with a bae that i a regular hexagon with ide length 5.5 cm; each triangular face ha equal ide with length 7.5 cm b) a right pyramid with a bae that i a regular pentagon with ide length.4 m and the ditance of each vertex from the centre of the bae i.0 m; the height i 3.9 m 0. A right cone ha a height of 8 ft. and a bae circumference of ft. Determine the urface area of the cone to the nearet quare foot.. A right pyramid ha a urface area of 58 cm. A right cone ha a bae radiu of 4 cm. The cone and pyramid have equal urface area. What i the height of the cone to the nearet tenth of a centimetre? Reflect What do you need to know to be able to calculate the urface area of a right pyramid and a right cone? Include labelled diagram in your explanation..4 Surface Area of Right Pyramid and Right Cone 35

6 .4 Surface Area of Right Pyramid and Right Cone, page a) 3 in. b) 0 cm 5. a) 68 in. b) 94 cm 6. a) 0 in. b) 649 cm 7. a) 5 in. b) 356 cm 8. a) 896 cm b) 68 yd. 9. a) b) 7008 ft ft.. a) 6.9 cm b) $ cm 3. a) 87 m b) 76 ft m ; I aumed the hide had equal area ft. 6. a) 69.0 mm b) 7.6 m 7. a) Right quare pyramid and right cone b) Right rectangular prim 8. The Louvre 9. a) 93.7 cm b) 34.9 m 0. 6 ft cm 46 ANSWERS