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A semi-circular sheet of paper of diameter 28cm is bent into an open conical cup. find the depth and capacity of the cup.
Let r cm and R cm be the radius of the semi-circular sheet and base of the conical cup respectively.
Suppose the depth of the conical cup is H cm.
Given, 2r = 2.8 cm
? r = 14 cm
When the semi-circular sheet of metal is bent into an open conical cup, then
Slant height of the cone, L = Radius of the semi-circular sheet = 14 cm
Circumference of base of cone = ?r
? 2?r = ?r = 14? cm
? 2R = 14 cm
? R = 7 cm
Slant height of the cone, L = 14 cm

? 49 cm2 + H 2 = (14 cm)2 = 196 cm2
? H 2 = 196 cm2 – 49 cm2 = 147 cm2


Thus, depth of the conical cup is


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