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.

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Solution

$A r e a o f c a n v a s = 551 m^{2} A r e a o f w a s t a g e = 1 m^{2} A c t u a l a r e a = 551 - 1 = 550 m^{2} B a s e r a d i u s o f t h e c o n i c a l t e n t = 7 m$

$L e t l b e t h e s l a n t h e i g h t a n d h b e t h e v e r t i c a l h e i g h t, t h e n s l a n t h e i g h t (l) = \frac{A r e a}{π r} = \frac{550 \times 7}{22 \times 7} = 25 m ∴ V e r t i c a l h e i g h t (h) = \sqrt{l^{2} - r^{2}} = \sqrt{25^{2} - 7^{2}} m = \sqrt{625 - 49} = \sqrt{576} m = 24 m N o w v o l u m e o f t h e t e n t = \frac{1}{3} π r^{2} h = \frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 24 m^{3} = 1232 m^{3}$

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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.