A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4cm. -Maths 9th

A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4cm. -Maths 9th
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Answer :

Let r1 and r2 Inner and outer radii of cylindrical pipe r1 = 4/2 cm = 2 cm r2 = 4.4/2 cm = 2.2 cm Height of cylindrical pipe, h = length of cylindrical pipe = 77 cm (i) curved surface area of outer surface of pipe = 2πr1h = 2×(22/7)×2×77 cm2 = 968 cm2 (ii) curved surface area of outer surface of pipe = 2πr2h = 2×(22/7)×2.2×77 cm2 = (22×22×2.2) cm2 = 1064.8 cm2 (iii) Total surface area of pipe = inner curved surface area+ outer curved surface area+ Area of both circular ends of pipe. = 2r1h+2r2h+2π(r12-r22) = 9668+1064.8+2×(22/7)×(2.22-22) = 2031.8+5.28 = 2038.08 cm2 Therefore, the total surface area of the cylindrical pipe is 2038.08 cm2. 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? (Assume π = 22/7) Solution: A roller is shaped like a cylinder. Let h be the height of the roller and r be the radius. h = Length of roller = 120 cm Radius of the circular end of roller = r = (84/2) cm = 42 cm Now, CSA of roller = 2πrh = 2×(22/7)×42×120 = 31680 cm2 Area of field = 500×CSA of roller = (500×31680) cm2 = 15840000 cm2 = 1584 m2. Therefore, area of playground is 1584 m2. Answer!
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