Question

Monica has a piece of canvas whose area is 551 $m^2$.She uses it to have a conical tent made,with a base radius of 7 m.Assuming that all the stitching margins and wastage incurred while cutting,amounts to approximately 1 $m^2$.Find the volume of the tent that can be made with it.

Answer 1

$Areaofcanvas=551m^{2}Areaofwastage=1m^{2}Actualarea=551-1=550m^{2}Baseradiusoftheconicaltent=7m$

$Letlbetheslantheightandhbetheverticalheight,thenslantheight\left(l\right)=\frac{Area}{\pi r}=\frac{550\times 7}{22\times 7}=25m\therefore Verticalheight\left(h\right)=\sqrt{l^2-r^2}=\sqrt{{25}^2-7^2}m=\sqrt{625-49}=\sqrt{576}m=24mNowvolumeofthetent=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24m^3=1232m^3$