Question

A conical tent of given capacity will require the least amount of canvas when the height is ....times the base radius

• A. $\sqrt{3}$
• B. 3
• C. 2
• D. $\sqrt{2}$

Answer 1

Answer: (D)

$\sqrt{2}$

$v=\frac{1}{3}\pi r^{2}h$

Surface area$=\pi rL$

$L^2=r^2+h^2$

$area=\pi {\left(\frac{3v}{\pi h}\right)}^{\frac{1}{2}}\sqrt{\frac{3v}{\pi h}+h^2}$

$area=\pi {\left(\frac{3v}{\pi }\right)}^{\frac{1}{2}}\sqrt{\frac{3v}{\pi h^2}+h}$

$\frac{d\left(area\right)}{dh}=c\frac{(\frac{-6v}{\pi h^3}+1)}{\sqrt{\frac{3v}{\pi h^2}+h}}$

$h=(\frac{6v}{\pi }{)}^{\frac{1}{3}}$

$r=\sqrt{2}(\frac{6v}{\pi }{)}^{\frac{1}{3}}$

$r=\sqrt{2}h$