Question
Mon March 09, 2015 By: Varsneya Srinivas

Respected sir/madam,
Can you please refer to Question No. 18 of Ex. 18.1 of the book RD Sharma. How do we find out the front surface area to be polished of the bookshelf?

Expert Reply
Vimala Ramamurthy
Tue March 10, 2015
G i v e n space t h a t space E x t e r n a l space l e n g t h space left parenthesis l right parenthesis space o f space b o o k s h e l f space equals space 85 space c m space space space space space E x t e r n a l space b r e a d t h space left parenthesis b right parenthesis space o f space b o o k s h e l f space equals space 25 space c m space space space space E x t e r n a l space h e i g h t space left parenthesis h right parenthesis space o f space b o o k s h e l f space equals space 110 space c m C u p b o a r d space i s space h a v i n g space 6 space f a c e s comma space f r o n t comma space b a c k comma space l e f t space s i d e comma space r i g h t space s i d e comma space t o p space a n d space b o t t o m. O f space w h i c h comma space w e space w i l l space l e a v e space t h e space f r o n t space s u r f a c e. W e space n e e d space t o space c a l c u l a t e space t h e space f r o n t space s u r f a c e space s e p a r a t e l y. E x t e r n a l space s u r f a c e space a r e a space o f space s h e l f space w h i l e space l e a v i n g space space space space space space space space space space space space space space space space space space space space space space f r o n t space f a c e space o f space s h e l f space equals space l h space plus space 2 space left parenthesis l b space plus space b h right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left square bracket 85 cross times space 110 space plus space 2 space left parenthesis 85 space cross times space 25 space plus space 25 cross times 110 right parenthesis right square bracket space c m squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 19100 space c m squared space A r e a space o f space f r o n t space f a c e space equals space left square bracket 85 cross times 110 space minus space 75 cross times 100 space plus space 2 space left parenthesis 75 cross times 5 right parenthesis right square bracket space c m squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1850 space plus space 750 space c m squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2600 space c m squared space space space space space A r e a space t o space b e space p o l i s h e d space equals space left parenthesis 19100 space plus space 2600 right parenthesis space c m squared space equals space 21700 space c m squared space space space space space space space space space C o s t space o f space p o l i s h i n g space 1 space c m squared space a r e a space equals space R s space 0.20 space space space space space C o s t space o f space p o l i s h i n g space 21700 space c m squared space a r e a space equals space R s space left parenthesis 21700 cross times 0.20 right parenthesis space equals space R s space 4340 space N o w comma space l e n g t h space left parenthesis l right parenthesis comma space b r e a d t h space left parenthesis b right parenthesis space h e i g h t space left parenthesis h right parenthesis space o f space e a c h space r o w space o f space b o o k s h e l f space i s space 75 space c m comma space 20 space c m comma space a n d space space space space space 30 c m open parentheses equals fraction numerator 110 minus 20 over denominator 3 end fraction close parentheses space space r e s p e c t i v e l y. space space space space space A r e a space t o space b e space p a i n t e d space i n space 1 space r o w space equals space 2 space left parenthesis l space plus space h right parenthesis space b space plus space l h space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left square bracket 2 space left parenthesis 75 space plus space 30 right parenthesis space space 20 space plus space 75 space space 30 right square bracket space c m squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 4200 space plus space 2250 right parenthesis space c m squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 6450 space c m 2 space A r e a space t o space b e space p a i n t e d space i n space 3 space r o w s space equals space left parenthesis 3 space space 6450 right parenthesis space c m squared space equals space 19350 space c m squared space C o s t space o f space p a i n t i n g space 1 space c m squared space a r e a space equals space R s space 0.10 C o s t space o f space p a i n t i n g space 19350 space c m squared space a r e a space equals space R s space left parenthesis 19350 space space 0.10 right parenthesis space equals space R s space 1935 space T o t a l space e x p e n s e space r e q u i r e d space f o r space p o l i s h i n g space a n d space p a i n t i n g space t h e space s u r f a c e space o f space t h e space b o o k s h e l f space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space R s left parenthesis 4340 space plus space 1935 right parenthesis space equals space R s space 6275
N o w space c o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
T h i s space i s space t h e space f r o n t space s u r f a c e space a r e a. S i n c e space t h e space t h i c k n e s s space o f space t h e space p l a n k space i s space 5 space c m comma space s u b t r a c t space 5 space c m space i n space l e f t comma space 5 space c m space i n space r i g h t comma space 5 space c m space i n space t o p space a n d space 5 space c m space i n space b o t t o m d i r e c t i o n s. T h u s space t h e space n e w space d i m e n s i o n s space o f space t h e space s h e e t space a r e space 85 minus 10 equals 75 space c m space a n d space 110 minus 10 equals 100 space c m A r e a space o f space t h e space w h o l e space s h e e t equals A r e a space o f space n e w space s h e e t plus A r e a space o f space p l a n k s S u b t r a c t space t h e space a r e a space o f space t h e space n e w space s h e e t space f r o m space t h e space o r i g i n a l space s h e e t. rightwards double arrow A r e a space o f space n e w space s h e e t equals A r e a space o f space t h e space w h o l e space s h e e t minus A r e a space o f space p l a n k s rightwards double arrow A r e a space o f space n e w space s h e e t equals 85 cross times 110 minus 75 cross times 100 N o w space y o u space w i l l space g e t space t h e space a r e a space o f space t h e space f o l l o w i n g space f i g u r e.
S i n c e space t h e r e space a r e space t w o space r a c k s space o f space t h i c k n e s s space 5 space c m space a n d space l e n g t h space 75 space c m space a r e space a d d e d space i n space b e t w e e n space t o p space a n d space b o t t o m comma w e space n e e d space t o space a d d space t h e space s u r a c e space a r e a space o f space t h e space f r o n t space f a c e s space o f space t h e space p l a n k s. T h a t space i s space w e space n e e d space t o space a d d comma space 2 cross times open parentheses 75 cross times 5 close parentheses space t o space t h e space a r e a space o f space f r o n t space f a c e. therefore A r e a space o f space f r o n t space f a c e equals 85 cross times 110 minus 75 cross times 100 plus space 2 cross times open parentheses 75 cross times 5 close parentheses
T h u s comma space t h e space t o t a l space s u r f a c e space a r e a space t o space b e space p o l i s h e d space i s equals open curly brackets 85 cross times 110 plus 2 open parentheses 85 cross times 25 plus 25 cross times 110 close parentheses close curly brackets plus A r e a space o f space f r o n t space f a c e equals open curly brackets 85 cross times 110 plus 2 open parentheses 85 cross times 25 plus 25 cross times 110 close parentheses close curly brackets plus 85 cross times 110 minus 75 cross times 100 plus space 2 cross times open parentheses 75 cross times 5 close parentheses
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