IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

kane

the altitude of a cone is 20cm and its semi-vertical angle is 30⁰.if the semi-vertical angle is increasing at the rate of 2⁰ per second,then the radius of the base is increasing at the rate of

answer:160/3 cm/sec

allamraju

For a cone,tank=r/h where k is the semi-vertical angle.

h=20cm $\Rightarrow$ r=htank $\Rightarrow$ dr/dt=(hsec²k)dk/dt=(20)(4/3)(2)=160/3cm/s

kane

thnxs a lot brother.i thought that altitude was slant height.how silly of me!!!!!!!!

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For a cone,tank=r/h where k is the semi-vertical angle.

h=20cmr=htankdr/dt=(hsec2k)dk/dt=(20)(4/3)(2)=160/3cm/s

h=20cm $\Rightarrow$ r=htank $\Rightarrow$ dr/dt=(hsec²k)dk/dt=(20)(4/3)(2)=160/3cm/s