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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-Minima- Word problemsMedium2 minQB

MathematicsMediumsingle choice

A right circular cone has volume $V_{1}$ . The largest right circular cylinder inscribed in it has volume $V_{2}$ . Find $V_{1} : V_{2}$ .

Options:

Answer:

Solution:

If the cone has radius $R$ and height $H$ , a cylinder of radius $r$ has height $h = H (R - r) / R$ . Maximizing $π r^{2} h$ gives $r = 2 R /3, h = H /3$ , and hence $V_{1} / V_{2} = 9/4$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima- Word problems

⏱ 2mℹ️ Source: QB

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