What is the length of the longest pole that can be placed in a cylindrical hall of diameter 12 m and height 5 m?

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Solution

Dear Student,

$T h e l e n g t h o f t h e l o n g e s t p o l e t h a t c a n b e p l a c e d i n a c y l i n d r i c a l h a l l w i l l b e g i v e n b y t h e d i a g o n a l o f t h e c y l i n d r i c a l h a l l . N o w, D i a m e t e r = d = 12 m, H e i g h t = h = 5 m ∴ D i a g o n a l = \sqrt{d^{2} + h^{2}} [U \sin g P y t h a g o r a s' T h e o r e m] = \sqrt{12^{2} + 5^{2}} = \sqrt{144 + 25} = \sqrt{169} = 13 m . T h u s, t h e l e n g t h o f t h e l o n g e s t p o l e t h a t c a n b e p l a c e d i n a c y l i n d r i c a l h a l l o f d i a m e t e r 12 m a n d h e i g h t 5 m i s 13 m .$

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