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Feb 27, 2014

# A semi circular sheet of metal of diameter 28 cm

Q. A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of cup.

Syeda

Member since Jan 25, 2017

Answer. Given diameter = 28 cm Radius, r = 14 cm Circumference of semi circle = πr = (22/7) x 14 = 44 cm This becomes circumference of base of cone 2πR = 44 R = 44 x (7/44) R = 7 cm The radius of semi circular sheet = slant height of conical cup That is l = 7 cm We know that r2 + h2 = l2 142 + h2 = 72 196 – 49 = h2 h2 = 147 Therefore, h = 7√3 cm That is depth of the conical cup is 7Ö3 cm Capacity of cup = (1/3) πr2h                               = (1/3) x (22/7) x 72 x 7√3                               = 622.37 cu cm

Kishore Kumar

Member since

depth and capacity of cup. Given diameter = 28 cm Radius, r = 14 cm Circumference of semi circle = πr = (22/7) x 14 = 44 cm This becomes circumference of base of cone 2πR = 44 R = 44 x (7/44) R = 7 cm The radius of semi circular sheet = slant height of conical cup That is l = 7 cm We know that r2 + h2 = l2 142 + h2 = 72 196 – 49 = h2 h2 = 147 Therefore, h = 7√3 cm That is depth of the conical cup is 7Ö3 cm Capacity of cup = (1/3) πr2h                               = (1/3) x (22/7) x 72 x 7√3                               = 622.37 cu cm (nearly)
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