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Question
A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.
Solution
Given, diameter of a semi-circular sheet = 28 cm
∴ Radius of a semi-circular sheet, r = `28/2` = 14 cm
Since, a semi-circular sheet of metal is bent to form an open conical cup.
Let the radius of a conical cup be R.
∴ Circumference base of cone = Circumference of semi-circle
2πR = πr
⇒ 2πR = π × 14
⇒ R = 7 cm
Now, `h = sqrt(l^2 - R^2)` ...[∵ l2 = h2 + R2]
= `sqrt(14^2 - 7^2)`
= `sqrt(196 - 49)`
= `sqrt(147)`
= 12.1243 cm
Volume (capacity) of conical cup = `1/3 piR^2h`
= `1/3 xx 22/7 xx 7 xx 7 xx 12.1243`
= 622.38 cm3
Hence, the capacity of an open conical cup is 622.38 cm3.
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