VOLUME & SURFACE AREA OF CYLINDER BY MAYANK AGNIHOTRI

O CYLINDER A cylinder is a 3-D solid or hollow body that is formed by keeping two circles of equal radii at two ends separated by a distance called height of cylinder. Cylinder is also formed by rolling a rectangular sheet along its side. A cylinder has three surfaces 1. Curved surface 2. Bottom 3. Top

1. SOLID CYLINDER Volume of cylinder Area of base x Height Tr2h Curved surface area = Perimeter of base x Height= 2MTh Total surface area = Curved surface area + Area of both the circles "To Where r radius of base &h- height

2. HOLLOW CYLINDER Volume of cylinder = Outer volume-inner volume-7R2h- 2h = h(R2-r2) . -Curved surface area Curved surface area of outer surface Curved surface area of inner surface Total surface area of cylinder = Curved surface area Area of both top and bottom surface Cntenal Radus 2T (R +r)(h + R-r) RCExtomal Radius) Where, R External radius of base,rInternal radius of base, h Height & Thickness -(R r)

Questions Ques 1. Two sheets of paper with measure 22 cm by 28 cm are taken. Each sheet is then rolled into a cylinder, one having the height 22 cm and the other of height 28 cm. The difference in their volumes (in cm) will be (1) 216 (2) 294 (3) 316 (4) 0 [CTET Feb 2016] Sol Circumference of first cylinder having 22 cm height will be 28 cm. Let radius be ri 28 m 2 71 : 28 28 28x7 49 Cm T 44 Circumference of second cylinder having 28 cm height will be 22 cm. Let radius be r2 22 C 2Tr2 22 = 22-22 7 r, 2 . Required difference in volume h2h2 ,2 [11 11 22-2 22 [49 , 49 7 L11 11 7 x 28-22 [4812-343- 22 [4802-3773 7 L 11 22x 1029 294 cm3 Ans 7

Ques 2. Two cylinders have equal volumes and their heights are in the ratio 1: 3. The ratio of their radii will be (1)1 3 (2)3 1 (3) V3:3 (4) 3 v3 So Let rand h be the radius and height of 1st cylinder r2 and h2 be the radius and height of 2nd cylinder. Given h1h2 1: Volume of 1st cylinder Trh Volume of 2nd cylinder Tr2 According to question, h = h2 2 1

Ques 3. A hollow garden roller of 42 cm diameter and length 152 cm is made of cast iron 2 cm thick. Find the volume of iron used in the roller. So. Diameter of the hollow garden roller 42 cm, Length (h) 152 cm diameter 42 inner radius (r) = =21 . cm 42 cm Thickness 2 cm iven] outer radius (R) inner radius + thickness 212 23 cm Volume of hollow cylinderth(R2 2) 2x 152(232 - 212) 152(529-441) = 72 152 88 -294 272=420388571 cm3 Ans = -

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Mayank Agnihotri

B.Tech (ECE), Machine enthusiast, Inspired by an old hindi saying " Gyan baatne se badhta ha"

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Manjit Singh

2 years ago

Article 31a, b,c removed and shifted to article 300a.. why so ? to remove them from under fundamental rights and simply place them under constitutional rights ? overall good lesson on fundamental rights, specially article 32 without which citizens cannot seek for remedies for violations the against fundamental rights. Thanks !

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Pallavi Chauhan

2 years ago

To remove the zamindari system which existed during the time of British rule, land distribution was needed. Redistribution of land was not possible due to Article 31 and any attempt towards doing so was challenged directly in supreme court as it was a FR. So many cases were filed against it and hence it got removed from FR.
Land acquisition is also a reason for its deletion from FR as most of the land aquisition is done by govt. only to set up industries. So govt wanted to correct the mistake it has done previously by removing it from the constitutional status.
Hope you got the idea!!

Manjit Singh

2 years ago

Yes got it, thanks!

Nitika Thakur

4 months ago

please check the answer again it's mot 294cm³ ( there should be 22/7*49/11*49/11*28......) but you have written something else.

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Mayank Agnihotri

4 months ago

can you please explain why it should be (22/7*49/11*49/11*28....) ? The height of first cylinder is 22 cm thats why its *22 and not *28 ...please listen the solution carefully before giving wrong comments.