Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 118104 by Lordose last updated on 15/Oct/20

1.) A right circular cone is circumscribed about a sphere of radius(r). If d is the distance from the center of the sphere to the vertex of the cone, show that the volume of the cone,V=((𝛑r^2 (r+d)^2 )/(3(d−r))). 2.) Find the vertical angle of the cone when it′s volume is minimum.

$$\left.\mathrm{1}.\right) \\ $$$$\mathrm{A}\:\mathrm{right}\:\mathrm{circular}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{circumscribed} \\ $$$$\mathrm{about}\:\mathrm{a}\:\mathrm{sphere}\:\mathrm{of}\:\mathrm{radius}\left(\boldsymbol{\mathrm{r}}\right).\:\:\mathrm{If}\:\boldsymbol{\mathrm{d}}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sphere} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone},\boldsymbol{\mathrm{V}}=\frac{\boldsymbol{\pi\mathrm{r}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{r}}+\boldsymbol{\mathrm{d}}\right)^{\mathrm{2}} }{\mathrm{3}\left(\boldsymbol{\mathrm{d}}−\boldsymbol{\mathrm{r}}\right)}. \\ $$$$\left.\mathrm{2}.\right) \\ $$$$\boldsymbol{\mathrm{F}}\mathrm{ind}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{when} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{volume}\:\mathrm{is}\:\mathrm{minimum}. \\ $$

Commented by 1549442205PVT last updated on 15/Oct/20

This is repeated question Q118069

$$\mathrm{This}\:\mathrm{is}\:\mathrm{repeated}\:\mathrm{question}\:\mathrm{Q118069} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com