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Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container. |
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Answer» Given: For cylindrical container: diameter (d) = 28 cm, height (h1) = 20 cm For cylindrical lid: height (h2) = 2 cm diameter (d) = 28 cm ∴ radius (r) = d/2 = 28/2 = 14 cm i. Surface area of the cylinder with one side open = Curved surface area + Area of a base = 2πrh1 + πr2 = πr (2h1 + r) = (22/7) x 14 x (2 x 20 + 14) = 22 x 2 x (40 + 14) = 22 x 2 x 54 = 2376 sq.cm ii. Area of sheet required to made a lid = Curved surface area of lid + Area of upper surface = 2πrh + πr2 = πr (2h + r) = (22/7) x 14 x (2 x 2 + 14) = 22 x 2 x (4 + 14) = 22 x 2 x 18 = 792 sq cm ∴ The area of the sheet required to make the cylindrical container is 2376 sq. cm and the approximate area of a sheet required to make the lid is 792 sq. cm. |
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