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Surface Areas and Volumes

Short Answer Type

41. A cylindrical vessel, without lid, has to be tin-coated including both of its sides. If the radius of its base is 1/2 m and its height is 1.4 m, calculate the cost of tin-coating at the rate of र 50 per 100 cm². (Use

straight pi

= 3.14)

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42. 10 cylindrical pillars of a building have to be painted. If the diameter of each pillar is 50 cm and the height 4 m, what will be the cost of painting at the rate of र 14 per square metre?

Diameter = 50 cm

therefore space space space Radius space left parenthesis straight r right parenthesis space equals space 50 over 2 space cm space equals space 25 space cm space space space space space space space space space space space space space space space space space space space space space equals space 25 over 100 space straight m space equals space 1 fourth space straight m

Height (h) = 4 m
∴ Curved surface area of 1 pillar = 2 $straight pi$ rh

equals 2 cross times 22 over 7 cross times 1 fourth cross times 4 equals 44 over 7 space straight m squared

Curved surface area of 10 pillars

equals 44 over 7 cross times 10 space straight m squared equals 440 over 7 space straight m squared

∴ Cost of painting at the rate of र 14 per square metre =

440 over 7 cross times 14

= र 880.

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43. A cylinder 3 m high, is open at the top. The circumference of its base is 22 cm. Find its total surface area.

open parentheses Take space straight pi space equals space 22 over 7 close parentheses

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44. Twenty cylindrical pillars of a building are to be cleaned. If the diameter of a pillar is 0.5 m and height is 4 m, what will be the cost of cleaning them at the rate of र 3 per m². (Take

straight pi

= 3.14)

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45. Find the curved surface area of a closed cylindrical petrol storage tank that is 3.8 m in diameter and 4.9 m high.

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46. 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 metre.

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47. The cost of painting the total outside surface of a closed cylindrical tank at 60 paise per sq. d.m. is र 237.60. The height of the tank is 6 times the radius of the base of the tank. Find its volume correct to two decimal places.

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48. Savitri had to make a model of a cylindrical kaleidoscope for her science project. She went to buy the chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius? You may take

straight pi equals 22 over 7.

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49. The radii of two right circular cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 4. Calculate the ratio of their curved surface areas.

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50. A cylindrical tower is 5 m in diameter and 14 m high. Find the cost of white-washing its curved surface at र 10 per square metre.

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