Question

the radius of the base of a right circular cone of semi vertical angle alpha is r find the volume of cone​

Answer 1

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Let height of cone be 'h', then in △OBA

tanα=OBOA=hr⇒h=tanαr=rcotα

Volume =31πr2h=31πr2.rcotα=31πr3cotα

CSA=πrl=πrr2+h2=πr=r2+(rcotα)2

=πrr2+r2cot2α=πrr2(1+cot2α)=πrr2csc2α

=πr.rcscα=πr2cscα