Question 1: The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder.
Answer: CSA of cylinder = 88 sq cm, h = 14 cm
CSA of cylinder `=2πr\h`
Or, diameter = 2 cm
Question 2: It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?
Answer: Diameter = 140 cm so, r = 70 cm, h = 100 cm
CSA of cylinder `=2π\rh`
`=2xx(22)/7xx70xx100=44000` sq cm
Area of top and bottom `=2πr^2`
`=2xx(22)/7xx70xx70=30800` sq cm
Total surface area of cylinder = 44000 + 30800 = 74800 sq cm = 7.48 sq m
Question 3: A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find its
(i) inner curved surface area,
Answer: h = 77 cm, r1 = 2 cm, r2 = 2.2 cm
Inner curved surface area `=2πrh`
`=2xx(22)/7xx2xx77=968` sq cm
(ii) outer curved surface area,
Answer: Outer curved surface area `=2πrh`
`=2xx(22)/7xx2.2xx77=1064.8` sq cm
(iii) total surface area.
Answer: Area of top `=πr_2^2-πr_1^2`
`=(22)/7xx4.2xx0.2=2.64` = area of bottom
Hence, total surface area = 968 + 1064.8 + 2.64 + 2.64 = 2038.04 sq cm
Question 4: The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2.
Answer: d = 84 cm, h = 120 cm
`=(22)/7xx84xx120=31680` sq cm = 3.168 sq m
Hence, area of playground `=3.168xx500=1584` sq m
Question 5: 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 m2.
Answer: d = 50 cm = 0.5 m, h = 3.5 m
CSA of cylinder `=π\dh`
`=(22)/7xx0.5xx3.5=5.5` sq m
Cost = Area × Rate `=5.5xx12.50` = Rs. 68.75
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