The frame of a lampshade is cylindrical in shape. It has base diameter 28 cm and height 17 cm. it is to be covered with a decorative cloth. A margin of 2 cm is to be given for folding it over top and bottom of the frame. If 1/12 of cloth is wasted in cutting and pasting, find how much cloth is required to be purchased for covering the frame.
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Solution:-
Diameter = 28 cm
Radius = 28/2 = 14 cm
Height = 17 cm
A margin of 2 cm is given for folding it over the top and bottom, so height is increased by (2 + 2) = 4 cm
Cloth required in covering = Lateral surface area = 2πrh
⇒ = 2*22/7*14*(17 + 2 + 2)
⇒ 2*22/7*14*21
⇒ 12936/7
⇒ 1848 cm²
Let total cloth purchased be 'x' cm
Cloth wasted = x/12
Therefore,
x = x/12 + 1848
⇒ 12x = x + 22176
⇒ 12x - x = 22176
⇒ 11x = 22176
⇒ x = 2016
Total cloth purchased is 2016 cm²
Answer.
Diameter = 28 cm
Radius = 28/2 = 14 cm
Height = 17 cm
A margin of 2 cm is given for folding it over the top and bottom, so height is increased by (2 + 2) = 4 cm
Cloth required in covering = Lateral surface area = 2πrh
⇒ = 2*22/7*14*(17 + 2 + 2)
⇒ 2*22/7*14*21
⇒ 12936/7
⇒ 1848 cm²
Let total cloth purchased be 'x' cm
Cloth wasted = x/12
Therefore,
x = x/12 + 1848
⇒ 12x = x + 22176
⇒ 12x - x = 22176
⇒ 11x = 22176
⇒ x = 2016
Total cloth purchased is 2016 cm²
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