1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold ? (1000 cm3 = 1 l) . 2. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g. Here, Inner diameter of the cylindrical pipe = 24 cm ⇒ Inner radius of the pipe (r) = (24/2) cm = 12 cm Outer diameter of the pipe = 28 cm ⇒ Outer radius of the pipe (R) = (28/2)cm = 14 cm Length of the pipe (h) = 35 cm ∵ Inner volume of the pipe = πr2h Outer volume of the pipe = πr2h ∴ Amount of wood (volume) in the pipe = Outer volume – Inner volume = πR2h - πr2h = πh(R2-r2) = πh(R+r)(R-r) [ ∵ a2 - b2 = (a+b)(a-b)] = 22/7 x 35 x (14+12) x (14-12) cm3 = 22 x 5 x 26 x 2 cm3 Mass of the wood in the pipe = [Mass of wood in 1 m3 of wood] x [Volume of wood in the pipe] = [0.6g] x [22 x 5 x 26 x 2] cm3 = (6/10)x 22 x 10 x 26 g = 6 x 22 x 26 g = 3432 g = (3432/1000)= 3.432 kg [∵ 1000 g = 1 kg] Thus, the required mass of the pipe is 3.432 kg. 3. A soft drink is available in two packs (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? For rectangular pack: Length (l) = 5 cm Breadth (b) = 4 cm Height (h) = 15 cm ∴ Volume = l x b x h = 5 x 4 x 15 cm3 = 300 cm3 ⇒ Capacity of the rectangular pack = 300 cm3 ...(1) For cylindrical pack: Base diameter = 7 cm ⇒ Radius of the base (r) = (7/2)cm Height (h) = 10 cm ∴ Volume = πr2h = (22/7) x (7/2)2 x 10 cm3 = (22/7) x (7/2) x (7/2) x 10 cm3 = 11 x 7 x 5 cm3 = 385 cm3 ⇒ Volume of the cylindrical pack = 385 cm3 ...(2) From (1) and (2), we have 385 cm3 – 300 cm3 = 85 cm3 ⇒ The cylindrical pack has the greater capacity by 85 cm3. 4. If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find: (i) radius of its base (ii) its volume. (Use π = 3.14) 5. It costs ₹ 2200 to paint the inner curved surface of cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹ 20 per m2; find: (i) inner curved surface of the vessel (ii) radius of the base (iii) capacity of the vessel. 6. The capacity of closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it ? 7. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite. 8. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients ?