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# Final maths ppt copy

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d pt is bout cylinders and deir prop as well as seir area n volume

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### Final maths ppt copy

1. 1. 0’CIRCULAR BASE AND Curved surfaceTOP ARE IDENTICAL 0
2. 2. W HAT IS A CYLINDER ?A SoLID gENERATED bY THEREvoLuTIoN of A RECTANgLE AbouToNE of ITS SIDES IS CALLED ACYLINDER.
3. 3.  CoNSIDER A CYLINDER WITH RADIuS R AND HEIgHT H. A CYLINDER HAS ATWo CIRCuLAR ENDS WHICH ARE PARALLEL .EACH of THESE IS CALLED bASE of THE CYLINDER. THE LINE SEgMENT JoININg THE CENTRES of THE TWo bASES IS CALLED THE AXIS of THE CYLINDER. THE PERPENDICuLAR DISTANCE bETWEEN THE TWo ENDS IS CALLED THE HEIgHT of THE CYLINDER.
4. 4. AREA of THE LATERAL SuRfACE of THE CYLINDER=AREA of THE RECTANguLAR STRIP of PAPER =AREA of A RECTANgLE of LENgTH 2*22/7*R =2*22/7*R*H =2*22/7*R*H SquARE uNITSTHuS foR A CYLINDER of RADIuS R AND HEIgHT H WE HAvE,LATERAL (CuRvED SuRfACE) AREA=2*22/7*R*H Sq uNITSToTAL SuRfACE AREA =(2*22/7*R*H+2*22/7*R*R)
5. 5. LET R and D BE THE EXTERNAL AND INTERNAL RADII OFCYLINDER ANDh BE ITS HEIGHT .1-SURFACE AREA OF EACH BASE=22/7(R*R-D*D)2-curved surface area=(external surface area )+(internalsurface area) =2*22/7*R*H+2*22/7*D*H =2*22/7*h(R+D) sq units3-total surface area =2*22/7*R*h+2*22/7*D*h+2*22/7(R*RD*D)
6. 6. EX 1-A RECTANguLAR SHEET of PAPER 44CM*18CM IS RoLLED ALoNg ITS LENgTH AND A CYLINDER IS foRMED. fIND THE RADIuS of THE CYLINDER. SoLuTIoN-WHEN THE RECTANguLAR SHEET IS RooLED ALoNg ITS LENgTH ,WE fIND THAT THE LENgTH of THE SHEET foRMS THE CIRCuMfERENCE of ITS bASE AND bREADTH of THE SHEET bECoMES THE HEIgHT of THE CYLINDER. LET R CM bE THE RADIuS of THE bASE AND HCM bE THE HEIgHT. THEN H=18CM CIRCuMfERENCE of THE bASE=L of THE SHEET oR 2*22/7*R=44 oR R= 7CM 44cm 18 cm18 cm
7. 7. EX -2A CoMPANY PACkAgES ITS MILk PoWDER IN CYLINDRICAL CoNTAINERS WHoSE bASE HAS A DIAMETRE of 16.8CM AND HEIgHT 20.5CM.CoMPANY PLACES A LAbEL ARouND THE CuRvED SuRfACE of THE CoNTAINER. If THE LAbEL IS PLACED 1.5CM fRoM THE ToP AND THE boTToM, WHAT IS THE SuRfACE AREA of THE LAbEL?SoLuTIoN—CLEARLY SuRfACE AREA of THE LAbEL IS EquAL To THE CuRvED SuRfACE AREA of A CYLINDER of bASE RADIuSR=16.8/2CM=8.4CMAND HEIgHT H=(20.5-1.5-1.5)CM=17.5CMTHEREfoRE SuRfACE AREA of THE LAbEL=2*22/7*8.4*17.5CM² =2*22/7*1.2*17.5CM²=924CM² 1.5CM 20.5C POWDERED MILK M 16.8 CM
8. 8. TAkE CIRCuLAR SHEETS of RADIuS R AND STuCk THEM uP vERTICALLY To foRM A CYLINDER of HEIgHT H.voLuME of THE CYLINDER=MEASuRE of THE SPACE oCCuPIED bY THE CYLINDER= r THE AREA of EACH CIRCuLARSHEET =22/7*R²H h
9. 9. Volume of a hollow cylinder=Exterior volume-interior R volume=22/7R²h-22/7r²h=22/7*h(R²-r²) h r
10. 10. A WELL WITH 10M INSIDE DIAMETER IS Dug ouT 14M DEEP. EARTH TAkEN ouT of IT IS SPREAD ALL ARouND To A WIDTH of 5MTo foRM AN EMbANkMENT. fIND ITS HEIgHT of EMbANkMENT.voLuME of THE EARTH Dug ouT=22/7*R²*H*M³=22/7*5*14M³=1100M³AREA of THE EMbANkMENT=22/7(R²-R²)=22/(10²-5²)M²=22/7*75M²THEREfoRE THE HEIgHT of THE EMbANkMENT=voLuME of THE EARTH Dug ouT/AREA of THE EMbANkMENT =1100/22/7*75=7*1100/22*75=4.66M 15m 10m
11. 11. EX-2:THE RAIN WATER THAT fALLS oN A Roof of AREA 6160M² IS CoLLECTED IN A CYLINDRICAL TANk of DIAMETER 14M AND HEIgHT 10M AND THuS THE TANk IS CoMPLETELY fILLED. fIND THE HEIgHT of RAIN WATER oN THE Roof.SoLuTIoN-LET THE HEIgHT of RAIN WATER oN THE Roof bE H METRE. CLEARLY RAIN WATER ACCuMuLATED oN THE Roof foRMS A CuboID of bASE AREA 6160M² AND HEIgHT H METRE.THEREfoRE THE voLuME of WATER ACCuMuLATED oN THE Roof= 6160*H M³THIS WATER CoMPLETELY fILLS A CYLINDER TANk of RADIuS 7M AND HEIgHT 10M.THEREfoRE WATER ACCuMuLATED oN THE Roof=voLuME of THE CYLINDER TANk=6160H=22/7*7²*10 oRH=1540/6160M=0.25M=25CMHENCE, THE HEIgHT of THE RAIN WATER oN THE Roof =25CM.
12. 12. Ex 3-how Many Cubic Metres Of Earth Must Be Dug Out To Sink A Well 22.5m Deep And Of Diametre 7m?Also,find The Cost Of Plastering The Inner Curved Surface At Rs3/M².Solution-volume Of Earth To Be Dug Out =Volume Of The Well =22/7*7/2*7/2*22.5 M³=866.25 M³Therefore,area Of Inner Curved Surface=2*22/7*r*h=2*22/7*7/2*22.5 M²=495m²Cost Of Platering The Inner Curved Surface =Rs (495*3)=rs 1485m²
13. 13. WRITTEN BY:ARISHA KHAN AND ANJALI JOSEPH ANIMATIONS BY :DRISHTI NIGAM AND DHEERAJ DINESH
14. 14. BACKGROUND MUSIC BY:DAN OWEN JONATHAN SPEAKER: BHARGAVI THAKUR
15. 15. THANK YOU