RS // TQ. Complete each proportion. V

Transcription

1 I. State the postulate or theorem that can be used to prove the s are similar II. Complete. 4a) ABC ~ 4b) 4c) 21 4d) AB AC BC D C E 21 A y = y = B III. In the fiure, it is iven that RS // TQ. Complete each proportion. V 5. a w 6. h p h a r w 7. r p h 8. p w T R h S p Q IV. Find the value of ABCD is a paralleloram. Find the values of and y. y D C A 16 1 B

2 REVIEW #2 1. Tell whether the proportion is correct. b j a. r a j s a n b. c. s b a r b t s r a d. t a r n b t e. f. k j s k j k t k n 2. Tell whether the proportion is correct. f a. d f e b. f e d c. e d e d. f d f d e

3 Chapter 11 - Solids Review 1. Find the volume and the total area of a cube with ede 2k. 2. A reular square pyramid has base ede 3 cm and volume 135 cm 2. Find the heiht. 3. A cone has radius 8 and heiht 6. Find the volume. 4. Find the lateral area and the total area of the cone in Eercise A riht trianular prism has a heiht 20 and base ede 5, and 13. Find the total area. 6. Find the volume of the prism in Eercise A cylinder has radius 6 cm and heiht 4 cm. Find the lateral area. 8. Find the volume of the cylinder in eercise 7.. A reular square pyramid has lateral area 60 m 2 and base ede 6 m. Find the volume.. A Sphere has radius 6 cm. Find the area and the volume. 11. Two cones have radii cm and cm and have slant heihts cm and 24 cm. Are the cones similar? Eplain. A reular pyramid has heiht and total area 648. A similar pyramid has heiht 6. Find the total area of the smaller pyramid. 13. The volumes of two similar rectanular solids are 00 cm 3 and 64 cm 3. What is the ratio of their lateral areas? 14. A cone and a cylinder each have radius 3 and heiht 4. Find the ratio of their volumes and of their lateral areas.. Find the volume of a sphere with area π m A cylinder with radius 7 has total area 168л cm 2. Find the heiht. 1. The diaonal of a cube is 16 3 cm. Find the total surface area. 3. Certain silver inots are cast in the shape of a riht prism whose base is a trapezoid. The bases of the trapezoid are 3 in. and 4 in. and the heiht of the inot is 2 in. The lenth of the inot is 1 ft. If the silver weihs 6 oz. per cubic inch, how much does one inot weih? 4. A storae bin is shaped as in the fiure. The radius of the cylindrical top is 7 ft. The overall heiht of the bin is 26 ft. and the altitude of the conical section is ft. Find the total surface area of the bin in bushels. 3

4 5. The dimensions of the base of a rectanular solid are 5 and 8, and its altitude is. A hole, etendin from upper base to lower base, is in the shape of a riht trianular prism whose bases are equilateral s havin an ede of 3. Determine the total surface area of the fiure. 1. Jimmy s lunch bo in the shape of a half cylinder on a rectanular bo. Find the total area of metal needed to manufacture it 2. A cistern (well) is to be built of cement. The walls and bottom will be 1 ft thick and painted with purple paint. The outer heiht will be 20 ft. The inner diameter is ft. How much paint is needed for the job? 8 3. A wede of cheese is cut from a cylindrical block. Find the total surface area of this wede A cylinder is cut on a slant as shown. Find the total suface area A rectanular prism is 40 ft by 38 ft by ft. Shown below is the prism with a half cylinder removed. Find the volume of the oriinal prism remainin. ft 6 38 ft ft ft ft ft Review Sheet Unless otherwise directed, leave all answers in terms of π or in simplest radical form. 1. A prism has 22 vertices. Determine the number of faces and edes. Find the total area and volume: 2. a reular heaonal prism with base edes of 8 cm and a lateral ede of 20 cm. 3. a cube whose base has a perimeter of 28 ft. 4. a prism with bases that are equilateral trianles with sides of cm and a lenth of 20 cm. 5. a cone that has radius 3 ft. and heiht 4 ft. 6. a cylinder with diameter of ft and heiht of ft. 7. a square pyramid which has a base with sides of 6 cm and a heiht of cm. 8. a sphere with diameter of 16 meters.. The area of the base of a riht cone is 144π sq cm and the heiht is 5 cm. Find the lateral area.. A cylinder with a 3 foot diameter is cut into a prism in which the bases are equilateral trianles with sides of 14 feet and a heiht of feet. Find the surface area of the fiure. 16. A sphere has a surface area of 0π square inches. Find the radius of the sphere. 17. Determine the surface area of the remainder of a cake that is 6 inches hih with a inch diameter after Mr. Harpst eats a 45 slice.. Find the amount of Saran wrap needed to cover a half of a rapefruit that is 5 inches in diameter 4

5 Review Sheet #1 Answers 1. SSS~ 2. AA~ 3. SAS~ 4a. EDC 4b. AB 4c. = 14 4d. y = 5. r 6. p 7. h 8. a. =. = = = =, y = 5.4 Review Sheet #2 1. a. no b. yes c. yes d. no e. yes f. yes 2. a. yes b. no c. yes d. no 3. = = = = = 8. = 30. = = = 4 = AC = BC ED EC DC 1. 8k 3 ; 24k cm LA: 80 TA: u u cm cm m 3. A: 144 cm 2 V: 288 cm No. TA: :4 14. V: 1:3 LA: 5:8 (not similar) cm # u allons oz bushels #2 500 u 2 1. a) u 3 b) u ft u TA: V = u in ,651.5 ft 3 Answers: All area problems should have square units, all volume are cubic units 1) 11 sides, 13 faces, 33 edes 2) LA = 60, SA = , V = ) LA = 16, SA = 24, V = 343 4) LA = 720, SA = , V = ) LA =, SA = 24, V = 36 6) LA = 0, SA = 200, V = 375 7) LA = 36 17, SA = , V = 432 8) SA = 256, V = 2048 /3 ) 6 ) balls are 32, cylinder is 48, wasted space is 16 11) (64 3)/3 ) volume is 335 cu feet, appro 251, 327 allons 13) SA = 1600, which is appro sq feet. Will take 16.75, or 17 allons of paint 14) Volume of cylinder is 8, volume of sphere is 256 /3. Wasted space is 8 /3 ) LA prism = 420, LA cyl = 30, top & bottom are /4, so SA = /2 16) r = 5 17) 770 / ) 75 /4 5