**Exercise 19.1**

**Question 1: Curved surface area of a right circular cylinder is 4.4 m**

^{2}. If the radius of the base of the cylinder is 0.7 m. Find its height.**Solution:**

^{2}

**Question 2: In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.**

**Solution:**

^{2}.

**Question 3: A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs 12.50 per m**

^{2}.**Solution:**

^{2}

^{2}area = Rs. 12.50 × 5.5

^{2}area = Rs. 68.75

**Question 4: It is required to make a closed cylindrical tank of height 1 m and the base diameter of 140 cm from a metal sheet. How many square meters of the sheet are required for the same?**

**Solution:**

^{2}.

**Question 5: A solid cylinder has a total surface area of 462 cm**

^{2}. Its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder.**Solution:**

^{2}

^{2}

^{2})/2r)=462

^{2})=462

^{2})=462×7/22

^{2}= 42 × 7

^{2}= 147

^{2}= 147 - 49

^{2}= 98

^{2}= 98/2

^{2}= 49

^{2}= √49

**Question 6: The total surface area of a hollow cylinder which is open on both the sides is 4620 sq.cm and the area of the base ring is 115.5 sq.cm and height is 7 cm. Find the thickness of the cylinder.**

**Solution:**

^{2}

^{2}

_{1}’ and ‘r

_{2}’ are the inner and outer radii of the hollow cylinder respectively.

_{2}

^{2}– πr

_{1}

^{2}= 115.5 …….(1)

_{1}h +2πr

_{2}h+ 2(πr

_{2}

^{2}– πr

_{1}

^{2}) = 4620

_{1}+ r

_{2}) + 2 x 115.5 = 4620

_{1}+ r

_{2}) = 4389

_{1}+ r

_{2}) = 313.5 ….(2)

_{2}

^{2}– πr

_{1}

^{2}= 115.5

_{2}+ r

_{1}) (r

_{2}– r

_{1}) = 115.5

^{2}– b

^{2}= (a – b)(a + b)]

_{2}– r

_{1}) = 115.5

_{2}– r

_{1}= 7/19 = 0.3684

**Question 7: Find the ratio between the total surface area of a cylinder to its curved surface area, given that height and radius of the tank are 7.5 m and 3.5 m.**

**Solution:**

**Question 8: The total surface of a hollow metal cylinder, open at both ends of an external radius of 8cm and height 10cm is 338cm**

^{2}. Take r to be the inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.**Solution:**

^{2}

^{2}

^{2}− 2πr

^{2}= 338π cm

^{2}

^{2}− r

^{2}) = 338π cm

^{2}

^{2}− r

^{2}) = 338π/2πcm

^{2}

^{2}− r

^{2}) = 169

^{2}= 169

^{2}= 169 – 80 - 64

^{2}= 25

^{2}− 10r + 25 = 0

^{2}− 5r − 5r + 25 = 0

**Question 9: A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs 3.50 per 1000 cm**

^{2}.**Solution:**

^{2})

^{2}

^{2}.

**Question 10: The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find:**

**(a) Inner curved surface area**

**(b) The cost of plastering this curved surface at the rate of Rs. 40 per m**

^{2}.**Solution:**

^{2}

^{2}area of the well is Rs. 40

^{2}area of the well

**Question 11: Find the lateral surface area of a petrol storage tank is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if 1/12th of the steel actually used was wasted in making the closed tank?**

**Solution:**

^{2}

^{2}

^{2}

^{2}steel actually used in making the tank = x-1x/12=(12x-1x)/12=11x/12

^{2}

^{2}

^{2}steel was actually wasted while constructing a tank.

**Question 12: The students of Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? (Take π = 3.14).**

**Solution:**

^{2}

^{2}

^{2}

^{2}of cardboard sheet for the competition.

**Question 13: The diameter of roller 1.5 m long is 84 cm.If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square meter.**

**Solution:**

^{2}

^{2}

^{2}

^{2}

^{2}= 50p = Rs. 0.5

^{2}= Rs. 396 × 0.5 = Rs. 198

**Question 14: Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50m and height is 4m.What will be the cost of cleaning them at the rate of Rs 2.50 per square meter?**

**Solution:**

^{2}

^{2}

^{2}

^{2 }

**Exercise 19.2**

**Question 1: 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?**

**Solution:**

^{3 }

^{3}

^{2}H

^{2}× 10cm

^{3 }

^{3}

^{3 }

^{3}

**Question 2: The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such pillars?**

**Solution:**

^{2}H

^{2}× 1000) cm

^{3}

^{3}

^{3}

^{3}= 17.6 m

^{3}

**Question 3: 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 cm**

^{3}of wood has a mass of 0.6 gm.**Solution:**

^{2}– r

^{2})h

^{2}– 12

^{2})35

^{3}

^{3}wood = 0.6 gm

^{3}wood = 5720 x 0.6 = 3432gm

^{3}wood is 3.432 kg.

**Question 4: If the lateral surface of a cylinder is 94.2 cm**

^{2}and its height is 5 cm, find: (i) radius of its base (ii) volume of the cylinder**Solution:**

^{2}

^{2}

^{2}h

^{2}× 5 cm

^{3}

^{3}

**Question 5: The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of the metal sheet would be needed to make it?**

**Solution:**

^{3}

^{2}h

^{2}h = 0.0154 m

^{3}

^{2}x 1 = 0.0154 m

^{3}

^{2}= 0.0154/3.14

^{2}

^{2}

**Question 6: 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?**

**Solution:**

^{2}h

^{2}× 4 cm

^{3}

^{3}

^{3}

^{3 }

**Question 7: A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.**

**Solution:**

^{2}−r

^{2})h

^{2}− (66)

^{2}}63

^{3}

**Question 8: A solid cylinder has a total surface area of 231 cm**

^{2}. Its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.**Solution:**

^{2}

^{2}

^{2}

^{2}= 231

^{2}= 231 (2πrh = 154cm

^{2})

^{2}= 231- 154

^{2}= 77

^{2}= (77 × 7)/(2 × 22)

^{2}= 49/4

^{2}

^{2}h

^{3}

^{3}

**Question 9: The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is Rs 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places.**

**Solution:**

^{2}is Rs. 198

^{2}h

^{3}

^{3}

**Question 10: The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes and the ratio of their curved surfaces.**

**Solution:**

**Question 11: The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the volume of the cylinder, if its total surface area is 616 cm**

^{2}.**Solution:**

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}

^{2}= 616 – 308

^{2}= 308

^{2}= 308/2π

^{2}= 49

^{2}

^{2}h

^{3}.

**Question 12: The curved surface area of a cylinder is 1320 cm**

^{2}and its base had diameter 21 cm. Find the height and volume of the cylinder.**Solution:**

^{2}

^{2}h

^{3}.

**Question 13: The ratio between the radius of the base and the height of a cylinder is 2:3. Find the total surface area of the cylinder, if its volume is 1617cm3.**

**Solution:**

^{3}

^{2}h

^{2}× 3x

^{2}× 3x

^{3}

^{3}

^{3}

^{3}

^{3}= 343/8

^{2}

^{2}.

**Question 14: A rectangular sheet of paper, 44 cm x 20 cm, is rolled along its length of form cylinder. Find the volume of the cylinder so formed.**

**Solution:**

^{2}h

^{3}.

**Question 15: The curved surface area of cylindrical pillar is 264m**

^{2}and its volume is 924m^{3}. Find the diameter and the height of the pillar.**Solution:**

^{2}

^{3}

^{2}h= 924

**Exercise VSAQs :-->**

**Question 1: Write the number of surfaces of a right circular cylinder.**

**Solution:**

**Question 2: Write the ratio of total surface area to the curved surface area of a cylinder of radius r and height h.**

**Solution:**

^{2})