A-cylindrical-iron-rod-8cm-and-6cm-in-diameter-stands-in-a-cylindrical-tin-of-12cm-in-diameter-Water-is-poured-into-the-tin-until-it-depth-is-8cm-How-far-would-the-level-drop-when-the-rod-is-remove

Question Number 5351 by sanusihammed last updated on 10/May/16

A c y l i n d r i c a l i r o n r o d 8 c m a n d 6 c m i n d i a m e t e r s t a n d s i n a

c y l i n d r i c a l t i n o f 12 c m i n d i a m e t e r . W a t e r i s p o u r e d i n t o t h e

t i n u n t i l i t d e p t h i s 8 c m . H o w f a r w o u l d t h e l e v e l d r o p w h e n t h e

r o d i s r e m o v e d ?

Commented by Yozzii last updated on 11/May/16

I a m g u e s s i n g t h a t t h e r o d a n d t i n s h a r e

t h e s a m e h e i g h t o f 8 c m, a n d t h a t t h e

h e i g h t o f t h e u p p e r e n d o f t h e r o d t h a t

i s a b o v e t h e t o p e d g e o f t h e t i n, w h e n

p l a c e d t o s t a n d i n t h e t i n, i s n e g l i g i b l e

t o g i v e a n a p p r o x i m a t e a n s w e r .

S o, t h e v o l u m e l e f t f o r t h e w a t e r i s

g i v e n b y V = π h (r_{t}^{2} - r_{r}^{2}) = π \times 8 (6^{2} - 3^{2}) = 216 π {c m}^{3} .

W h e n t h e w a t e r i s a d d e d, i t s v o l u m e

i s a p p r o x i m a t e l y 216 π {c m}^{3} . S o w h e n t h e

r o d i s r e m o v e d t h e w a t e r s e t t l e s, t a k i n g

u p a v o l u m e o f a b o u t 216 π {c m}^{3} s t i l l w i t h

b a s e r a d i u s e q u a l t o 6 c m .

S o, f o r s o m e h \Rightarrow π {h r}_{t}^{2} = 216 π \Rightarrow h = \frac{216}{6^{2}} = 6 c m .

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