Question The surface area of a right-circular cone of radius r and height h is S = Ar Vp2 + h2, and its volume is V = #ph. (a) Determine h and r for the cone with given surface area S = 4 and maximal volume V. h = r (b) What is the ratio h/r for a cone with given volume V = 6 and minimal surface area S? h T (c) Does a cone with given volume V and maximal surface area exist? A. no B. yes
Solection: The surfall area S=pi rsqrt(h^(2)+r^(2)) cond volum r=(1)/(3)pir^(2)h{:[AV(r","h)=(pi)/(3)(:2rh,r^(2):)],[x+g(r","h)=x(:pisqrt(r^(2)+h^(2))+(pi r(2r))/(2sqrt(r^(2)+h^(2))),(pi r(2h))/(2sqrt(r^(2)+h^(2))):)]:}lambda grad g(r,h)=lambda(:(pi(2r^(2)+h^(2)))/(sqrt(r^(2)+h^(2))),(pi rh)/(sqrt(r^(2)+h^(2))):)write eqtias the corsting adinelyse the cots r edtion to form a syltu of epsias,{:[(pi)/(3)2rh=lambda(2r^(2)+h^(2))/(sqrt(r^(2)+h^(2)))-(-1)],[(pi)/(3)r^(2)=(lambda pi rh)/(sqrt(r^(2)+4^(2)))],[" तr "sqrt(r^(2)+h^(2))=4],[(2gamma hsqrt(r^(2)+h^(2)))/(3(2sqrt2^(2)+h^(2)))=(gammasqrt(r^(2)+h^(2)))/(3h)],[h^(2)=2r^(2)],[" nav "pi rsqrt(3r^(2))=4],[" or "Pisqrt3r^(2)=4=>r=(2)/((pisqrt3)^(1//2))],[" or "h^(2)=2xx(4)/(pisqr ... See the full answer