3 MENSURATION TASK cm. 8 cm 12 cm. x cm. 30 m. 20 m. 24 m. 40 m

Transcription

1 1 3 MENSURTIN TSK 3.1 Give nswers to one deciml plce if necessry. Find the re of ech shpe elow. ll lengths re in cm The re of the prllelogrm is equl to the re of the trpezium. Find the vlue of x. x cm 6 cm 6 cm 5. Find the shded re. 30 m 20 m 40 m 24 m 6. Find the shded re.

2 Mensurtion 2 7. Find the re of ech shpe. ll rcs re either semi-circles or qurter circles nd the units re cm. c Find ech shded re elow. ll lengths re in cm. 28 c circulr pond hs rdius of 13 m. pth goes ll the wy round the circumference of the pond. The pth is 1 2 m wide throughout. Find the re of the pth. 10. Clculte the rdius of circle of re The re of this prllelogrm is cm 2. Clculte the vlue of x. x Find the re of this regulr pentgon cm TSK cm cm cm Find the re of ech tringle elow, giving the nswer to one deciml plce.

3 Mensurtion 3 Find the vlue of the letter in ech tringle elow cm cm 14 3 cm re = 13 5 cm 2 re = 75 cm 2 c 8 7 cm re = 55 cm 2 7. re tringle C = 4 2 re tringle D = 120 cm 2 Clculte the length of CD. 17 cm D C x The re of this tringle is equl to the re of this trpezium. Clculte the vlue of x. 6 cm 5 cm TSK Wht is the rdius of circle if the dimeter is 46 cm? Wht is the dimeter of circle if the rdius is 19 mm? Use clcultor to find the circumference of ech circle elow (give nswers to 1 d.p.) c d 3 m 17 m 4. Which shpe hs the lrger perimeter the tringle or the circle? 5 cm 6 cm

4 Mensurtion 4 5. Which circle hs the lrger perimeter? 7 cm Clculte the perimeter of ech shpe. ll rcs re either semi-circles or qurter circles. Give nswers correct to 1 d.p cm 31 cm 5 cm 5 cm m 32 m m 3 m 6 m 12. circulr log of dimeter 30 cm is rolled down hill. It rolls 48 metres. How mny complete revolutions did the log mke efore it stopped? 13. Sn hs ike with wheels of rdius 31 5 cm. She cycles 3 km. How mny times do the wheels of her ike go round completely?

5 Mensurtion 5 TSK cm cm Clculte the re of ech circle elow, correct to 1 d.p. 5. circulr pond hs rdius of 11 m. Wht is the re of this pond in m 2? 6. Which shpe hs the lrger re the tringle or the circle? 5 cm 1 5 cm 3 cm 7. Find the shded re In Questions 8 to 10 find the re of ech shpe. ll rcs re either semi-circles or qurter circles nd the units re cm. Give nswers correct to 1 d.p

6 In Questions 11 to 13 find the shded re. Lengths re in cm. Give nswers correct to 1 d.p Mensurtion circulr pond hs rdius of 13 m. pth goes ll the wy round the circumference of the pond. The pth is 1 2 m wide throughout. Find the re of the pth. TSK 3.5 In this tsk, is lwys the centre of the circle. Give nswers to 1 d.p. 1. Find the length of rc. 2. Find the length of rc. 15 cm 65 7 cm cm The rc PQ =. Find ngle PQ. P Q 15 cm

7 In Questions 4 to 6, find the perimeter of ech shpe, leving nswers in terms of p Mensurtion cm 3 cm 7. Use clcultor to find the perimeter of the shded re. 29 D 5 cm C 8. Use clcultor to find the perimeter of the shded re TSK 3.6 In this tsk, is lwys the centre of the circle. Give nswers to 1 d.p. In Questions 1 to 3, find ech shded re cm cm 7 cm 78

8 Mensurtion 8 4. Show tht the re of this sector is exctly 16p DC is sector of rdius. Find the shded re, leving your nswer in terms of p. C 80 D 10 cm 10 cm 6. Find the vlue of if the re of the sector is 90 cm Find the re of the shded segment. 5 cm If = 13 cm, find the re of the shded segment.

9 Mensurtion 9 TSK 3.7 Rememer 1m 3 = 1000 l = cm 3 1m 2 = cm 2 1. Find the volume of ech prism elow: 6 m 4 m 3 cm 9 m 3 m 25 cm 12 m 13 cm 2. Which is the greter mount? 7 2 m 3 or cm 3 3. True or flse? 6 3 m 2 = 630 cm 2 4. rectngulr tnk hs length of 8 m nd width of 6 m. How high is the tnk if it cn hold litres of wter when full? 5. Copy nd complete 4m 3 = cm m 3 = cm 3 c 8m 2 = cm 2 d 7 48 m 2 = cm 2 e cm 3 = m 3 f 6m 3 = litres g cm 2 = m 2 h 5 16 m 3 = litres i cm 2 = m 2 6. Find the exct volume of ech prism elow, leving your nswers in terms of p. 10 cm 3 cm 7. pipe of dimeter nd length 3 m is hlf full of wter. How mny litres of wter re in the pipe?

10 Mensurtion Find the volume of this prism. 21 cm 9. cylindricl ucket hs dimeter of 30 cm nd height of 35 cm. How mny full ucket lods of wter re needed to fill up the tnk opposite? 45 cm 60 cm 10. The height of cylinder of cpcity 3 5 litres is twice its rdius. Clculte the rdius of the cylinder. 85 cm TSK 3.8 Rememer sphere pyrmid cone volume = 4 3 pr3 volume = 1 3 (se re) h volume = 1 3 pr2 h In this tsk, give nswers to 3 significnt figures where necessry. 1. Find the volume of ech solid. 1 4 m c 2 5 m 23 cm 3 m 2. hemisphere nd cone re oth mde from the sme mteril. The cone hs se dimeter of nd perpendiculr height of 6 cm. The hemisphere hs dimeter of 7 cm. Which solid weighs more? 7 m

11 Mensurtion sphere hs volume of 80 cm 3. Find the rdius of the sphere. 4. Find the exct volume of ech solid, leving your nswers in terms of p. 3 cm 16 cm 25 cm 15 cm (hemisphere on cylinder) 5. owl is in the shpe of hemisphere with dimeter 1. Wter is poured into the owl t rte of 3 /s. How long will it tke to fill the owl completely? 6. pyrmid hs squre se of side length nd perpendiculr height of 17 cm. The pyrmid hs the sme volume s cone of se rdius 6 5 cm. Find the perpendiculr height of the cone. 7. metl cylinder hs dimeter 4 nd height of 8 3 cm. 75 identicl cylinders re melted down to mke single sphere. Clculte the dimeter of the sphere. TSK 3.9 Rememer sphere cylinder cone surfce re=4pr 2 curved surfce re=2prh curved surfce re=prl where l is the slnt height In this tsk, give nswers to 3 significnt figures where necessry. 1. Find the curved surfce re of ech solid. c 1 23 cm 1

12 Mensurtion Find the totl surfce re of this cone, leving your nswer in terms of p. 10 cm 3. sphere hs surfce re of 480 cm 2. Clculte its dimeter. 4. The curved surfce re of hemisphere is 72p cm 2. Wht is the totl surfce re of the hemisphere? 5. cone is ttched to cylinder of dimeter 15 cm s shown. The perpendiculr heights of the cylinder nd the cone re oth equl to the dimeter of the cylinder. Find the totl surfce re of the comined solid. 15 cm 6. cylinder hs rdius of 2 cm nd height of 10 cm. cone hs rdius of 3 cm. The totl surfce re of the cone is equl to the totl surfce p re of the cylinder. Show tht the perpendiculr height of the cone is 4 ffiffiffiffiffi 10 cm. TSK 3.10 Use M DV to help you work out the questions elow. 1. solid weighs 450 g nd hs volume of 50 cm 3. Find the density of this solid. 2. liquid hs density of 2 g/cm 2. How much does the liquid weigh if its volume is 240 cm 3? 3. metl r hs density of 12 g/cm 3 nd mss of 360 g. Find the volume of the metl r. 4. Copy nd complete this tle. density (g/cm 3 ) mss (g) volume (cm 3 )

13 Mensurtion Gold hs density of 19 3 g/cm 3. gold ring hs volume of 1 1 cm 3. Find the mss of the gold ring. 6. rss hndle hs volume of 17 cm 3 nd mss of g. Find the density of the rss. 7. Which hs greter volume g of led with density 11 4 g/cm 3 or g of steel with density 8 3 g/cm 3? Write down y how much. 8. The density of this metl r is 7 4 g/cm 3. Find the mss of this metl r. Give your nswer in kg. (Note the length is given in metres.) 9. metl cue of length 0 2 m hs density of 8 3 g/cm 3. hole is ored through the cue with 485 cm 3 of metl eing removed. Wht is the mss in kg of the remining piece of metl? 5 cm 1 2 m 10. metl r hs 3 holes cut completely through its length. The cross-sectionl re of ech hole is y cm 2. The density of the metl is 9 g/cm 3. Find the mss of the remining piece of metl, giving your nswer in terms of x nd y. 7 cm x cm x cm