Surface Area of a Sphere

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(1)Surface Area of a Cone SA. =. nr?. +. ttrs. Volume of a Cone. V=. Surface Area of a Sphere. Surface Area of a Cylinder. SA = 4rrr2. Volume of a Sphere. SA = Znr?. Zttrli. Volume of Square/Rectangular Pyramid. V=. V=. UNIT CONVERSIONS Ift, = 12 in. lino. = 2.5. cm. lyd. = 3 ft. 1 mi. = 1760 yd.. +. Irni. = 1.6 km. lwh 3.

(2) 1'/". Chapter 1 Study Guide Skill. Description. Convert between units in the imperial system.. Use the relationships the units.. Convert between units in the imperial system and the SI system.. Use the relationships between he systems.. Find the slam height or heigh of a cone.. Use the Pythagorean Theorem.. Example between. Convert: 19 yd. to feet 1 yd. = 3 ft. 19 yd. = 19 x 3 ft. 19 yd. = 57ft. Convert: 37 rni. to kilometres. 1 mi. == 1.6 km 37 mi. == 37 x 1.6 km 37 mi. == 59.2 km To the nearest centimetre, height of this cone.. find the. ,. 26 cm. :h. 14 cm. ,. ---------~:::-:::~ 262 = 142 h2 = 262 -. +. h2 142. h=J262-142 h = 21.9089 ... The height is about 22 cm. Find the surface areas of pyramids, prisms, cones, cylinders, and spheres.. For a pyramid or a prism, add the area of the base or bases to the area of the faces. For a cone or a cylinder, add the area of the base or bases to the curved surface area. Surface area of a sphere is: 41T(radius)2. To the nearest square foot find the surface area of a cylinder with radius 3 ft. and height 9 ft. SA = 2nr2 + 2nrh SA = 2n(3)2 + 21T(3)(9) SA = 226.1946 ... The surface area is about 226 square feet.. Find the volumes of prisms, cylinders, pyramids, cones, and spheres.. Volume of a prism and a cylinder is: (base area)(height) Volume of a pyramid and a cone is:. To the nearest cubic inch, find the volume of a cylinder with radius 2 in. and height 8 in. V = 1Tr2h V = 1T(2)2(8) V = 100.5309 ... The volume is about 101 cubic inches.. t(baSe area)(height) Volume of a sphere is: ~1T(radiuS)3. 60. 978-0-321-62414-7. a-. Copyright © 2011 Pearson Canada lnc..

(3) Chapter 2 Study Guide Skill. Description. Find a triqonornetric ratio.. InMBC,. Example. AB. hypotenuse. side adjacent 0Voppos;teLA A. C. si. A. =. opposite hypotenuse. Find the measure of an angle.. =. 8. . A = sin. adjacent cos A =-....:.....-hypotenuse tan A. -. opposite hypotenuse. -!...!---. . A BC Sin = AB. op~osite adjacent. 6 sin A = 1 0' or 0.6. To find the measure of an acute angle in a right triangle: 1. Use the given lengths to write a trigonometric ratio. 2. Use the inverse function on a scientific calculator to find the measure of the angle.. To find the measure of LB in L>ABC above: opposite tan B = . adjacent tan B = AC BC. =~. tan B. LB LB Find the length of a side.. C. = ==. tan-l(~) 53°. To find the length of EF in L>DEF:. To find the length of a side in a right triangle: 1. Use the measure of an angle and the length of a related side to write an equation using a trigonometric ratio. 2. Solve the equation.. E~. 3.0C:~F. f. adjacent cos E = hypotenuse DE cos E =EF. 3.0. cos 64° =EF EF cos 64° = 3.0 EF = EF =. 3.0 cos 64° 6.8435 .... EF == 6.8 cm 978-0-321-62414-75.. Copyright. © 2011 Pearson Canada Ine.. 127.

(4) Unit 1 Measurement. Review. Section 1.1 1:. Identify the most appropriate. imperial unit to estimate each of the following,. and state which. referent you would use. A) The width of the classroom B) The greatest width of a maple leaf. C) The length of your friend's shadow. 2:. Convert... A) B) C) D) E). 8 ft to inches 235 yards to feet 6 mi to yards 72 in. to feet 87 ft to yards. F) G) H) I) J) K). 288 in. to yards 67 in. to feet and inches 418 ft. to yards and feet 2148 in. to yards and feet 7ft. 5 in. to inches 9 yd. 1 ft. to feet. 3:. Sue wants to fence part of her yard. perimeter in feet?. She measures the perimeter. as 44yd.. What is the. 4:. A dog trainer advises that, when walking a dog on a city street, the walker should allow the dog 42in. of leash. Greg bought a retractable leash that extends 5 Yz yd. Greg follows the trainer's advice. What length of the leash, in inches, is not used?. 5:. A mural is 3yd. long and 2yd. wide.. It has a border that is made with sections that are 48in.. long. How many sections were needed to make the border? Section 1.2 6:. Convert.. .. A) 5 in. to centimetres B) 8 ft. to meters C) 7 mi. to kilometres D) 12m to inches E) 7km to miles F) 86 cm to inches. 7:. Tammy drove 85km to a camp site. Todd drove 52mi. to meet Tammy at the camp site. Who drove farther?. Justify your answer..

(5) 8:. To qualify for the school olleyball try-outs, Rick needs to be able to jump and touch a line on a wall that is 8ft. 2in. off the ground. In his workouts, Rick jumped 243cm. Will he qualify for the try outs?. Section 1.4 9:. Find the surface area of each object to the nearest square unit.. /. 6 in.. 8m. 20cm. 10:. A triangular pyramid has 4 congruent faces. Each face has a base length of 12cm and a height of 10.4cm. Find its surface area.. 11:. Find the slant height of this cone to the nearest tenth of a unit.. 12:. A wooden square pyramid is to be painted.. The side length of the base is 8cm and the height of. the pyramid is 6cm. To the nearest square centimetre,. what is the area that will be painted?. 13:. A cone-shaped hat is to be made with radius Sin. and height 12in. To the nearest square inch, how much material will be need for the hat?. 14:. A triangular. pyramid has 4 congruent faces. The surface area is 250 square inches. Find its slant. height to the nearest tenth of an inch. Section 1.5 15:. Find the volume of each object to the nearest cubic unit.. /. \ L---.. 5cm12····. 3cm. ~\9ft.C '. 14m. cm. 5m 12m. \'1 \. /. ./i.

(6) 16:. Find the volume of a square pyramid that has a base length of 8in. and a slant height of 12in.. 17:. Find the volume of a cone that has a diameter of 22in and a slant height of 14in.. 18:. The base of a square prism has a side length 8cm and height of 12cm.. The base of a square. pyramid has a side length of 12cm and height of 17cm. Which object has the greater volume? 19:. Both a cylinder and a cone have volume 1525 cubic inches and base radius 7in. Find the height of each object to the nearest tenth of an inch.. 20:. A rectangular pyramid can hold 1250 cubic feet of water. 10ft. What is the height of the pyramid?. The base of the pyramid is 15ft. by. Section 1.6 2:. Find the surface area AND volume of each of following ... A). Sphere with radius 2ft.. B) Sphere with diameter 17cm Cl Hemisphere with radius 11 in. D) Hemisphere with diameter 5m 22:. A ball has a surface area of 28 square inches. Find the radius of the ball, to the nearest tenth of an inch.. 23:. A disco ball is covered in 9 square feet of silver foil. To the nearest inch, what is the diameter of the ball?. Section 1.7 24:. Find the surface area of each of the following composite objects.. ~~. 1'------------1 I. 14 ft. I. I. \. 6 ft.. 3 ft. 4 ft.. 25:. A sphere of flavoured ice is served in a cylinder shaped paper cup. The cup has diameter 6cm and height lOcm. The sphere has the same diameter as the cup. To the nearest cubic centimetre, how much space is left inside the cup? (hint: one half of the sphere is below the rim of the cup.).

(7) 26:. Find the volume of each of the following composite objects.. ;=J. 8ern. s.ocm. 15.0cm.

(8) Unit 2 Trigonometry Review Section 2.1 1: Find the tangent ratio for the indicated angle. y. 3. x 2:. 7. Find the measure of LA for each value of tan A. Give your answer to the nearest degree. A) Tan A =0.5. 5 6. B) Tan A = ~ 3:. A telephone pole is 18m high and is supported by a wire 8m from the base. What angle, to the nearest degree, does the wire make with the ground?. 4:. Victor is building a wheelchair ramp to an entranceway that is 3m above the sidewalk. The ramp will cover a horizontal distance of SOm. What angle to the nearest degree, will the ramp make with the ground?. Section 2.2. 5:. Find the length of each indicated side.. x. G. ?. H. 6:. F . ?. 6 ern. A rope supports a tent. The angle between the rope and the level ground is 59°. The rope is attached to the ground 1.2m from the base of the tent, At what height above the ground is the rope attached to the tent? Give your answer to the nearest tenth of a metre,. Section 2.3 7:. Use the information. C II'MW'.e.JW. in the diagram to find the height of tree to the nearest tenth of a metre.. ~(~::. ---~. 1.7m. Q. ~Of). -. --------------,. P•.~:-----------------------l. -:. j. ~. -. 10m. \.. ~. jrJR.

(9) Section 2.4 8:. Find the measure of each indicated angle to the nearest degree.. A. c. y. B. 5.5 cm. F. 9:. A firefighter rests a lS.6m ladder against a building. What angle does the ladder make with the ground, if the ladder is 8.Sm away from the base of the building?. 10:. A loading ramp is 4.Sm long. The top ofthe ramp has height 1.6m. What angle does the ramp make with the ground? Give your answer to the nearest degree.. Section 2.5 11:. .. Find the length of each indicated side to the nearest tenth of a centimetre .. W. R. ?. ?. v. u. E. s. Q. W. 21.6 cm G. y. 8.4 cm. M. ?. P. 12:. N. A straight slide in a playground makes an angle of 28° with the ground. The slide covers a horizontal distance of 4.Sm. How long is the slide? Give your answer to the nearest tenth of a metre.. 13:. A lSm support cable joins the top of a telephone pole to a point on the ground. The cable makes an angle of 32° with the ground. Find the height of the pole to the nearest tenth of a meter..

(10) Chapter 3 Study Guide. ,.. Skill. Description. Example. Write the prime factorization of a number.. Write the prime factors of a number as a product.. The prime factorization 2 x 3 ;( 3, or 2 x 32. Find the greatest common factor (GQ) two numbers.. List the factors of each number. Identify the greatest factor that is in bo h lists.. Find the GCF of 12 and 16: Factors of 12: 1,2,3,4,6,12 Factors of 16: 1, 2, 4, 8, 16 The GCF of 12 and 16 is 4.. Find the least common multiple (LCM) of two numbers.. List multiples of each number. Identify the least multiple that is in both lists.. Find the LCM of 12 Multiples of 12: 12, Multiples of 16': 16, The LCM of 12 and. Find the square. root of a perfect square and the cube root of a perfect cube.. Group the prime factors.. Find /64: 64 = (2 x 2 x 2) x (2 x 2 x 2) /64 = 2 x 2 x 2, or 8. ..... _------. of. of 18 is:. and 16: 24, 36, 48, 60, ... 32, 48, 64, 80, ... 16 is 48.. Find %4: 64 = (2 x 2) x (2 x 2) x (2 x 2) %4 = 2 x 2, or 4. ~.

(11) . -.e ~ e prime factorization of 144 and 600 2:. Find he GCF of each pair of numbers: A) 44 and 70 B) 36 and 48. 3:. Find the LCM of each pair of numbers: A) 12 and 30 B) 16 and 18. 4:. Hamburger. patties come in packages of 8.. Buns come in packages of 6.. number of hamburgers that can be made with no patties or buns left over? Section 3.2 5:. Use prime factorization. A). --/225. B). --/196. to find each square root. Cl J1225 6:. Use prime factorization. A). to find each cube root.. 3,}729. B) 3,}3375 C). 3,}9261. Section 4.2 7:. Tell whether each number is rational or irrational.. A) 8:. B). Find each square root.. A) 9:. 136. 14. B). Find each cube root. A). V-216. B). D). C) Identify any that are irrational.. C). J9. D). Identify any that are irrational.. C). 3,}1. D). What is the least.

(12) Section 4.3 10:. 11:. Simplify each radical.. A). J320. E). if40. B). J735. F). \1162. C). -J24. G). \1189. D). Ms. H). \1576. Write each mixed radical as an entire radical.. A). 3m. C). B). 2Jl3. D). 3\14 2V15.

(13) Chapter 4 Study Guide Skill. Description. , Example. I---------t-------------+---. Classify radicals as rational or irrational numbers.. Simplify a radical.. Write a mixed radical as an entire radical.. .. -------------i. A radical is rational if it can be written as: a fraction, a terminating decimal, or a repeating decimal.. Classify each radical as rational or irrational.. Write the radicand as a product with a perfect power as one factor. Then write the radical as the product of a whole number and a radical.. Simplify.. Write the whole number as the root of a perfect power. Then multiply the perfect power and the radicand to get the new radicand.. 215 as an entire 2 = ~2 ·2 . 2, or 18 50, 215 = 18 . 15. = 1.5, so .fi.25 is rational. )2.25. j2 =. !2 is irrational. 1.4142 ... , so. J24. J24=~. = J4· j6 =. 2/6. Express. radical.. ~ rs-:s. =140 Write a power with a rational number exponent as a radical.. The numerator of the exponent is the power to which the base is raised. The denominator of the exponent is the index of the radical.. Write a power with a negative exponent as a power with a positive exponent.. Write the reciprocal of the base, and change the exponent from negative to positive.. Apply exponent laws to simplify expressions.. The exponent laws apply for rational and integer exponents and bases, and for variable bases. The expression is usually written with positive exponents.. 2. Express. i3 as a radical.. 2. i =F 2 or i3 = (17)2 3. Write each power with a positive exponent.. (~)-4 (~)4 =. Simplify. 1. x -Z . x-2 =. -.!.-2 X. 2 1. = x -Z-Z. 4. 5. =. x-Z, or~ X2. 244. 978-0-321-62414-75.. Copyright © 2011 Pearson Canada Ine..

(14) Chapter 4 Puzzle How Irrational. Is It? 3. The radical .)26 and the power. i'i went. to a bank to apply for credit cards.. "I'm sorry," said the bank manager, "You may not have credit cards." "Why not?,". ,. asked the radical and power, "Is it because we are irrational?". Why did the bank manager not give them credit cards? To find out, evaluate or simplify each expression below. Then, write the matching. letter above the matching answer on the underline below.. =U. N= 3. 42. =. = E. =. =H. 1. 22. =. 5-3. =Y. 2. 33 =. =A. (~r2. =. 2-5.. 24 =. =N = R. 5-3 . 54 5. 2. =1. =8'. (4~r 1. 72 .. 1. i4 =. =T. (2l2~t = 4.fP j2. 8. 125. -. 8. 16. =0. 19. 1 125. j2. iP. -8. -. -. 1 8 2. 8. -2. 16 9. 32. 1 2. 16 9. 978-0-321-62414-7. --------. 8. 15- Copyright. ©. 2011 Pearson Canada Ine.. 243.