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A wooden bookshelf has externaldimensions as follows: Height = 110 cm, Depth =25 cm, Breadth = 85 cm (see figure). The thickness ofthe plank is 5 cm everywhere. The external faces are to be polished and inner faces are to be painted. If the rate of polishinb is 20 paise per cm² and the rate of painting is 10 paise per cm², find the total expenses required for polishing and painting the surface of the bookshelf.​

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327 cents Watts
Answer:

\large{\underline{\underline{\bf{Required\:Answer:}}}}

\huge{\boxed{\bf{\red{₹6275}}}}

\large{\underline{\underline{\bf{Step\:by\:step\:explanation:}}}}

Surface area to be polished

:\implies{\sf{\big[(110 \times 85) + 2(110\times25) + 2(85\times25)}}

\displaystyle{\sf{\:\:\:\:\:\:\:\:+ 2(110 \times 5 + 4(75 \times 5)\big]}}

:\implies{\sf{(9350+5500+4250+1100+1500)cm^{2}}}

:\implies{\boxed{\sf{\purple{21700\:cm^{2}}}}}

{\therefore} Expenses required for polishing @ 20 paise per cm²

\displaystyle{\sf{\:\:\:\:\:\:\:\:=\:21700\times 20\:paise}}

\displaystyle{\sf{\:\:\:\:\:\:\:\:=₹ \frac{21700\times 20}{100}}}

⠀⠀⠀⠀⠀⠀⠀⠀:\implies{\boxed{\sf{\orange{₹4340}}}}

Surface area to be painted

\longrightarrow{\sf{\big[2(20\times90) + 6(75\times20) + (75\times 90)\big]}}

\longrightarrow{\sf{(3600+9000+6750)cm^{2}}}

:\implies{\boxed{\sf{\purple{19350\:cm^{2}}}}}

{\therefore} Expenses required for painting @ 10 paise per cm²

\displaystyle{\sf{\:\:\:\:\:\:\:\:=\:19350\times 10\:paise}}

\displaystyle{\sf{\:\:\:\:\:\:\:\:=₹ \frac{19350\times 10}{100}}}

⠀⠀⠀⠀⠀⠀⠀⠀:\implies{\boxed{\sf{\orange{₹1935}}}}

{\therefore} Total expenses required for polishing and painting the surface of the bookshelf

:\implies{\sf{₹\:4340\:+\:₹\:1935}}

\large{:}\implies{\boxed{\bf{\red{₹6275}}}}

Hence, the total expenses required for polishing and painting the surface of the bookshelf is ₹6275.

And we are done! :D

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