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