4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A
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1 Geometry: Shpes. Circumference nd re of circle HOMEWORK D C U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter cm e Dimeter 6. cm f Rdius 3. John runs twice round circulr trck which hs rdius of 50 m. How fr hs he run? Give your nswers in terms of π. rolling pin hs dimeter of. Wht is the circumference of the rolling pin? How mny revolutions does it mke when rolling length of 30 cm? How mny complete revolutions will icycle wheel with rdius of 8 cm mke in journey of 3 km? Clculte the re of ech of these circles, giving your nswers to deciml plce, except for nd d, where your nswer should e in terms of π. Rdius cm Dimeter cm c Rdius 9 cm d Dimeter m e Rdius cm f Dimeter 0.9 cm Wht is the totl perimeter of semicircle of dimeter? Give your nswer to dp. Wht is the totl perimeter of semicircle of rdius? Give your nswer in terms of π. circle hs circumference of cm. Wht is its dimeter? grden hs circulr lwn of dimeter 0 m. There is pth m wide ll the wy round the circumference. Wht is the re of this pth? Clculte the re of semicircle with dimeter of. Give your nswer to dp. circle hs n re of 50 m. Wht is its rdius? I hve circle with circumference of. Wht is the re of this circle? Jne wlked round circulr lwn. She counted 53 pces to wlk round it. Ech of her pces ws out cm. Wht is the re of the lwn? Clculte the re of this shpe. 0 cm UNIT 3 FM Functionl Mths U (O) ssessing Understnding PS (O3) Prolem Solving
2 CHPTER : Geometry: Shpes FM 5. re of trpezium The dimeter of cycle wheel is 70 cm. How mny metres will the cycle trvel if the wheel mkes 50 revolutions? C HOMEWORK B Clculte the perimeter nd the re of ech of these trpeziums. D cm. cm 0 cm 9 cm 3 cm Clculte the re of ech of these shpes. 7 m 0 cm 3 m m 5 m 3 m 8 cm 3 cm cm 3 Which of the following shpes hs the lrgest re? 3 cm 8 cm.. cm U Clculte the re of this trpezium cm UNIT 3 5
3 CHPTER : Geometry: Shpes D FM 5 This is the pln of n re tht is to e seeded with grss. 6 m 3 m m C PS 6 7 m Seed should e plnted t rte of 30 g per m. How much grss seed will e required? trpezium hs n re of 00 cm. The prllel sides re nd 3 cm long. How fr prt re the prllel sides? Clculte the re of the shded prt in ech of these digrms. cm cm 8 cm 3 cm cm 9 cm cm 8 Wht percentge of this shpe hs een shded? 3 cm 0 cm.3 Sectors HOMEWORK C For these sectors, clculte the rc length nd the sector re cm Clculte the rc length nd the re of sector whose rc sutends right ngle in circle of dimeter 0 cm. Give your nswer in terms of π UNIT 3
4 CHPTER : Geometry: Shpes 3 Clculte the totl perimeter of ech of these shpes. cm 0 cm Clculte the re of ech of these shpes. 0 8 cm 5 9 cm 5 There is n infrred sensor in security system. The sensor cn detect movement inside sector of circle. The rdius of the circle is 6 m. The sector is 0. Clculte the re of the sector. 6 m 0 6 m U 6 circle of rdius 8 cm is cut up into five congruent sectors. Clculte the perimeter of ech one. Sensor FM 7 PS 8 shelf to fit in the corner of room is to e cut in the shpe of qurter of circle. It will e cut from squre of wood of side 30 cm. Wht will e the re of the shelf? BCD is squre of side length. PC nd QC re rcs of the circle with centres D nd B. Clculte the re of the unshded prt. P B * Q D C. Volume of prism HOMEWORK D For ech prism shown, clculte the re of the cross-section nd the volume. C 5 m m m m 6 m m 0 m 3 m 5 m UNIT 3 7
5 CHPTER : Geometry: Shpes C B U FM 3 U chocolte ox is in the form of tringulr prism. It is 8 cm long nd hs volume of Wht is the re of the tringulr end of the ox? wooden door wedge hs cross-section which is this shpe: 3 cm The wedge is 3 cm wide. Clculte the volume of wood needed to mke the wedge. If the wedge is cut from lock of wood (cuoid) mesuring 3cm 3cm, wht volume of wood is wsted? Which of these solids is: the heviest the lightest? i (.6 g/cm 3 ) ii iii (3.3 g/cm 3 ) (.35 g/cm 3 ) cm.5 Cylinders cm cm cm HOMEWORK E B 3 Find i the volume nd ii the curved surfce re of cylinder with se rdius nd height cm. Give your nswer in terms of π. Find i the volume nd ii the curved surfce re of cylinder with se rdius 8 cm nd height. Give your nswer to suitle degree of ccurcy. Find i the volume nd ii the totl surfce re of ech of these cylinders. 0 cm 0 cm Wht is the rdius of cylinder with height of nd volume of π cm 3? Wht is the rdius of cylinder with height of 0 cm nd curved surfce re of 360π cm? Wht is the height of cylinder with dimeter of cm nd volume of 08π cm 3? cylinder of height 0 cm hs curved surfce re of 00 cm. Clculte the volume of this cylinder. 8 UNIT 3
6 CHPTER : Geometry: Shpes 8 9 U 0 FM PS Clculte the curved surfce re of cylinder which hs height of 8 cm nd volume of 390 cm 3. cylinder hs the sme height nd rdius. The totl surfce re is 00π. Clculte the volume. Give your nswer in terms of π. squre of pper of side 0 cm is ent round to mke cylindricl shpe y putting two edges together. Wht is the volume of the cylinder? cylindricl food cn must hve volume of t lest 00 cm 3 in order to hold the correct mount. The dimeter of the cn hs to e. Wht is the smllest possile height of the cn? Metl cylinders re mde y ending rectngulr sheets of metl mesuring long y wide until the sides meet. How mny cylinders cn e mde from sheet of metl tht is m long nd m wide? B.6 Volume of pyrmid HOMEWORK F U 3 5 Clculte the volume of ech of these pyrmids, oth with rectngulr ses. Clculte the volume of pyrmid tht hs squre se of side 0 cm nd verticl height of 8 cm. n octhedron is mde y fixing together the two squre ses of two identicl pyrmids. Ech pyrmid is 9 cm high nd hs se with ech side. Clculte the volume of the octhedron. The Khufu pyrmid in Egypt ws originlly 6 m tll. Ech side of the squre se ws 30 m long. It ws uilt from limestone locks with density of out.7 tonnes per cuic metre. It proly took 0 yers to complete. Estimte the totl weight of the locks used to uild the pyrmid. Clculte the volume of this shpe. 6 m 30 cm 3 m 3 cm B 6 m 5 m UNIT 3 9
7 CHPTER : Geometry: Shpes 6 Clculte the height h of rectngulr-sed pyrmid with length of cm, width of 0 cm nd volume of 0 cm 3. h 0 cm cm V = 0 cm 3 * 7 The pyrmid in the digrm hs its top cut off s shown. The shpe which is left is clled frustum. Clculte the volume of the frustum..7 Cones HOMEWORK G For ech cone, clculte i its volume nd ii its totl surfce re. (The units re cm.) Find the totl surfce re of cone of which the se rdius is cm nd slnt height is. Give your nswer in terms of π. Find the volume of cone of which the se rdius is nd verticl height is 8 cm. Give your nswer in terms of π. In order to mke cone, sector of ngle 60 is cut from circle with rdius of cm. Clculte the circumference of the se of the cone. Clculte the rdius of the se of the cone. c Stte the length of the slnt height of the cone. d Clculte the curved surfce re of the cone. e Clculte the verticl height of the cone. f Clculte the volume of the cone. 60 cm U 5 cone with se dimeter of hs the sme volume s cue of side cm. Find the height of the cone. 30 UNIT 3
8 CHPTER : Geometry: Shpes FM 6 U 7 PS 8 Cndy needs to mke conicl ht to go with her fncy dress costume. She knows tht the circumference of the ht is 60 cm, nd tht she hs to cut the mteril in the shpe of sector of circle. She lso knows tht the slnt edge of the conicl ht is 30 cm. Help Cndy to work out the re of the mteril she needs to mke the ht. continer in the shpe of cone, se rdius 0 cm nd verticl height 9 cm, is full of wter. The wter is poured into n empty cylinder of rdius. How high is the wter in the cylinder? The digrm shows pper cone. The dimeter of the se is.8 cm nd the slnt height is cm. The cone is cut long the line V nd opened out flt, s shown elow. * V cm V z.8 cm Clculte the size of ngle z..8 Spheres HOMEWORK H U 7 FM 8 Clculte the volume of spheres with the following mesurements. Give your nswers in terms of π. Rdius 3 cm Dimeter 30 cm Clculte the surfce re of spheres with the following mesurements. Give your nswers in terms of π. Rdius cm Dimeter 0 cm Clculte the volume nd the surfce re of sphere with dimeter of 30 cm. Give your nswers to suitle degree of ccurcy. Clculte, correct to one deciml plce, the rdius of sphere: with surfce re of 00 cm with volume of 00 cm 3 The volume of sphere is 50 m 3. Find its dimeter. Wht is the volume of sphere with surfce re of 00 cm? cue of metl of side hs hemisphericl hole of dimeter cm cut into it. Wht is the volume of the resulting shpe? roller skte mnufcturing compny needs to mke mm-dimeter steel ll erings. How mny ll erings cn the compny mke from one cuic metre of steel? UNIT 3 3
9 CHPTER : Geometry: Shpes * 9 spinning top, which consists of cone of se rdius, slnt height 0 cm nd hemisphere of rdius, is illustrted on the right. Give your nswers in terms of π. Clculte the volume of the spinning top. Clculte the totl surfce re of the spinning top. 0 cm Functionl Mths ctivity Pckging sweets sweets mnufcturer wnts new pckge for n ssortment of sweets. The pckge must hve volume of 000 cm 3 in order to hold the sweets. The chosen design will e prism. The length hs een specified s 0 cm. The cross-section of the pckge will e one of three possiilities: squre, n equilterl tringle or circle. You hve een sked to investigte the mount of pckging mteril needed for ech design, s this will ffect the cost of mnufcture. Clculte the surfce re of ech of the three designs. Comment on how much difference there is etween the three surfce res nd how this could ffect production costs. This formul could e useful: The re of n equilterl tringle of side is 3 3 UNIT 3
10 nswers: New GCSE Mths Q Modulr Homework Book Higher Geometry: Shpe. Circumference nd re of circle HOMEWORK 9. cm 3. cm c 50.3 m d.0 cm e 0. cm f.0 cm 00π complete revolutions 5 6π cm 53.9 cm c 5. d π m e 385. cm f cm 7 6π cm 9 66 m cm 3.99 m m 8 cm 5 0 metres. re of trpezium HOMEWORK B 3. cm, 8 cm 3, m = 0 cm ; = 9. ; so hs the lrgest re 5 5 out 3 kg 6 7 cm 8 6.7%.3 Sectors HOMEWORK C 8., 3. cm, 38..5π 6.5π 3 5. cm cm m 6 6. cm Unshded prt is 96. HrperCollins Pulishers Ltd 0
11 nswers: New GCSE Mths Q Modulr Homework Book Higher. Volume of prism HOMEWORK D 0.5 m, m 3 5 m, 50 m cm 3 3 i is the heviest (90 g) ii is the lightest (87.8 g) (iii weighs 89 g).5 Cylinders HOMEWORK E i 00π cm 3 ii 0π cm i 300 cm 3 ii 850 cm 3 i 78 3 ii i 393 cm 3 ii 3 cm cm 5 8 cm 6 3 cm 7 59 cm π cm cm cylinders.6 Volume of pyrmid HOMEWORK F 70 cm cm cm cm million tonnes 5 0 cm cm Cones HOMEWORK G i 80 cm 3 ii 53 cm i 30 cm 3 ii 30 cm 0π cm 3 96π cm cm 0 cm c cm d 0π cm e 0π cm 3 f 6.63 cm cm HrperCollins Pulishers Ltd
12 nswers: New GCSE Mths Q Modulr Homework Book Higher cm 7.8 cm Spheres HOMEWORK H 36π cm 3 500π cm 3 6π cm 00π cm 3 Volume = 000 cm 3, surfce re = 800 cm.0 cm cm cm 8 out π cm 3 3π cm Functionl Mths ctivity Pckging sweets Cuoid Tringulr prism Cylinder Side length Rdius 3.99 cm Surfce re cm Differences etween the three surfce res: tringulr prism is 79 cm lrger thn the cuoid nd cm lrger thn the cylinder cuoid is 6 lrger thn the cylinder. How surfce re ffects production costs: the lrger the surfce re, the more pckging mteril tht is required therefore the higher the production costs. HrperCollins Pulishers Ltd
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