An open conical cup is formed from a thin metallic semi-circular sheet – InterviewSolution

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1.	An open conical cup is formed from a thin metallic semi-circular sheet of diameter 28 cm. Find its volume.
Answer» Radius of semi-circle `R=(28)/(2)=14 cm` Length of arc of semi-circle `=pi R=(22)/(7)xx14=44 cm` Let radius of cone = r `therefore 2pi r=44cm` `rArr r = (44)/(2pi)cm` `rArr r=(44)/(2xx(22)/(7))=7cm` The radius of semi-circule will be equal to the slant height of cone `thereforel=R=14 cm` Now, `h^(2)=l^(2)-r^(2)=14^(2)-7^(2)` = 196 - 49 = 147 `rArr h = sqrt(147)=7sqrt(3)cm` `therefore` Volume of cup `= (1)/(3)pi r^(2)h` `=(1)/(3)xx(22)/(7)xx7xx7xx7sqrt(3)cm^(3)` `=(1078xx1.732)/(3)=622.36 cm^(3)`

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