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InterviewSolution
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The numerical values of the volume and the lateral surface area of a right circular cone are equal. If the height and the radius of the cone are h unit and r unit respectively , then find the value of `(1)/(h^2)+(1)/(r^2)`. |
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Answer» Let the slant height of the right circular cone is l unit . Also the height and radius of the cone are h and r unit respectively. As per question , `(1)/(3)pi r^2h=pi rl` or `rh=3lrArr r^2h^2=9 l ^2rArr r^2h^2=9 (h^2+r^2)` `rArr (h^2+r^2)/(r^2h^2)=(1)/(9)rArr (h^2)/(r^2h^2)+(r^2)/(r^2h^2)=(1)/(9)rArr (1)/(r^2)+(1)/(h^2)=(1)/(9)rArr (1)/(h^2)+(1)/(r^2)=(1)/(9)` Hence the value of `(1)/(h^2)+(1)/(r^2)=(1)/(9)`. |
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