A. V = lwh where l = 11, w = 8 and h = 2 = = 88 2 = 176 cm 3. b) Find the volume of the cube. =... m 3 = = cm 3
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1 5. [Voume] Ski 5.1 rectanguar prism square prism cube Cacuating te voume of square and rectanguar prisms. engt widt eigt w engt widt eigt engt engt engt w MM MM Q. Te parce is a rectanguar prism. Wat is te voume of te parce? cm A. w were 11, w 8 and cm 11 cm 8 cm a) Find te voume of te square prism. b) Find te voume of te cube. 4 mm 6 mm.5 mm were.5 and mm mm c) Given tat te diswaser is a square prism, find its voume. 0.8 m d) Find te voume of te buiding bocks stack. 5 cm 5 cm 5 cm 0.6 m 0.6 m m cm page 9 Mats Mate 5./6.1 Ski Buider 5
2 Ski 5. Cacuating te voume of oter prisms (1). MM MM Find any unknown side engts. Cacuate te area of te base. Use known formuae were possibe. Hint: Te eigt of a triange is needed to cacuate te area of a triange and soud not be confused wit te eigt () of te prism. Substitute known vaues into te formua: prism Area of base eigt of prism A b A b Q. Find te voume of te trianguar prism using A b. 14 cm cm 5 cm A. A b 1 A b b cm eigt of prism eigt of triange First cacuate area of base a) Find te voume of te prism. b) Using Area of base (A b ) eigt (), find te voume of te prism. 6 mm Base 10 mm A b were 10 mm A b dased sides mm A b cm 11 cm A b mm cm c) Using A b find te voume of te exagona prism. d) Find te voume of te trianguar prism using A b. 15 mm 5 mm A b 5 m 8 m 10 mm A b m A b A b mm page 94 Mats Mate 5./6.1 Ski Buider 5
3 Ski 5. Cacuating te voume of oter prisms (). MM MM e) Find te voume of te prism. f) Find te voume of te prism. base is a triange m 0 mm 1.5 m 1 mm m 4 mm A b First cacuate area of base 1 A b m A b mm g) Find te voume of concrete used to buid te steps. ) Find te voume of te prism. 15 cm m A b cm 1 cm A b m cm i) Find te voume of te prism. j) Find te voume of te prism. m 11 cm 0 cm 1 cm m 11 m 4 m A b cm A b m page 95 Mats Mate 5./6.1 Ski Buider 5
4 Ski 5. Cacuating te voume of pyramids. MM MM Substitute known vaues into te appropriate formua to find te area of te base. Substitute known vaues into te voume formua: pyramid 1 Area of base eigt of pyramid A b Base w A b Q. Find te voume of te square pyramid. A. A b m m m Simpify: A a) Using b find te voume of te trianguar pyramid of eigt 6 cm. A b) Using b find te voume of te trianguar pyramid. 6 cm 14 cm 9 cm A b 1 m 9 m A b 1 1 A b b A b A b cm m c) Find te voume of te square pyramid. d) Find te voume of te trianguar pyramid. 11 mm 1 m 0 m 9 mm 6 m A b A b mm m page 96 Mats Mate 5./6.1 Ski Buider 5
5 Ski 5.4 Cacuating te voume of basic -dimensiona round sapes. MM MM Substitute known vaues into te appropriate formua: cyinder πr r cone πr r spere 4πr r Q. Using πr and π, find te voume of te cyinder. 14 mm 0 mm A. πr were r and mm Simpify: 4πr a) Using and π.14, find te voume of te spere. b) Using πr and π, find te maximum voume of te gass. 5 mm 100 mm 6 cm 4πr were r cm Simpify: cm πr c) Using and π.14, find te voume of te cone. mm 4πr d) Using and π.14, find te voume of te spere, correct to decima paces. m 8 m 0 cm m cm page 9 Mats Mate 5./6.1 Ski Buider 5
6 Ski 5.5 Expressing te voume of -dimensiona sapes in agebraic form. MM MM Substitute vaues into te appropriate formua for voume. (see skis 5.1 to 5.4, pg. 9 to 9) Adapt te formuas were necessary. Q. Write an agebraic expression for te voume V of te sape. [Express te answer in terms of a and π.] 4a 8a 5a A. V sq. prism were 5a and 4a 5a 5a 4a 100a 1 V af cy. πr were r a and 4a 1 π 9a 4a 18πa V sape 100a + 18πa a (50 + 9π) a) Write an agebraic expression for te voume V of te sape. [Express te answer in terms of d and π.] 8d b) Write an agebraic expression for te voume V of te prism. [Express te answer in terms of x.] 5x d 5d V cy πr π d 5d 5πd r d and d πr V cone 1 π d d πd V sape 5πd + πd r d and 5d c) Write an agebraic expression for te voume V of te obeisk. [Express te answer in terms of k.] 8x d) Write an agebraic expression for te voume V of te sape. [Express te answer in terms of a and π.] 5k a a e) Write an agebraic expression for te voume V of te capsue. [Express te answer in terms of x and π.] 8x 6x k f) A rectanguar box contains identica candes paced wit no room to move. Write an agebraic expression in terms of x and π for te voume of te box wic is not occupied by te candes. x x page 98 Mats Mate 5./6.1 Ski Buider 5
7 Ski 5.6 Cacuating voume in reation to capacity. MM MM Substitute known vaues into te appropriate formua. Use te conversion factors between cubic units and capacity units: Conversion Facts - CUBIC VOLUME to CAPACITY 1000 cm 1000 ml 1 L 1000 L 1 m Q. A rectanguar swimming poo is 0 m ong and 1 m wide. If its average dept is m, ow many itres of water woud you need to fi te poo? [Hint: 1000 L 1 m ] a) Te vase as 0.5 itre of water in it. Find te dept of te water. [Hint: 1000 cm 1 L] A. w were 0, w 1 and m Convert m to L L b) A rectanguar fis tank wit dimensions 0 cm by 15 cm by 10 cm is af fu of water. How many miiitres of water woud you need to fi te fis tank? [Hint: 1 ml 1 cm ] 5 cm were 5 and Using 0.5 L 500 ml cm ml πr c) Using and π.14, find ow muc ice cream coud fit exacty inside tis cone. [Hint: 1 ml 1 cm ] 6 cm d) Using π find te maximum voume of water te troug coud od. [Hint: 1000 cm 1 L] 150 cm 1 cm 0 cm ml L page 99 Mats Mate 5./6.1 Ski Buider 5
8 Ski 5. Cacuating voume in reation to engt and area. MM MM Substitute known vaues into te appropriate formuas for area and voume. Q. A rectanguar prism wit voume 16 cm as a eigt of 6 cm and a widt of 5 cm. Cacuate te engt of te prism. A. w were 16, w 5 and Divide 1.6 by. cm a) A cube as a tota surface area of 54 cm. Wat is te voume of te cube? TSA 6 and so 9 and 6 n a cube: w cm c) If a cube as a tota surface area of 96 mm, wat is te voume of te cube? b) A rectanguar prism wit voume 189 mm as a eigt of mm and a engt of mm. Cacuate te widt of te prism. mm d) If a cube as a tota surface area of 150 cm, wat is te voume of te cube? mm e) A rectanguar ong jump pit ods 1.5 m of sand. If te pit is 9 m ong and m wide, ow deep is te sand? cm f) How many meta cubes of side engt 4 mm need to be meted down to produce a singe cube of side engt 8 mm? m... g) A rectanguar fis tank can od cm wen fu. If te tank is 0 cm wide and 0 cm ong, ow deep is te water? ) How many meta cubes of side engt cm need to be meted down to produce a singe cube of side engt 9 cm? cm... page 00 Mats Mate 5./6.1 Ski Buider 5
9 Ski 5.8 Cacuating te voume of composite soids. MM MM Substitute vaues into te appropriate formuas for voume. Q. A 0 mm 0 mm 0 mm pyramid is removed from a 0 mm 0 mm 0 mm cube. Find te voume of te remaining sape. 0 mm a) How muc ess is te voume of te cone tan te voume of te cyinder of te same eigt? (Use π ) A. V 1 of cube A V of square pyramid b were A b and V 1 V were Simpify: mm b) A emispere of diameter 1 m is removed from tis cyinder. Using π find te voume of te remaining sape. cm 0 m V 1 of a cyinder πr, V of a cone V 1 V πr 11 1 Simpify 11 cm c) Using π.14 find te voume of te sape. mm 1 cm 10 mm πr πr 1 πr mm m d) A cone of diameter 6 cm and eigt 14 cm is removed from tis cyinder. Find te voume of te remaining sape. (Use π ) 14 cm 6 cm 1 m cm page 01 Mats Mate 5./6.1 Ski Buider 5
10 page 0 Mats Mate 5./6.1 Ski Buider 5
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