Question

A wooden bookshelf has external
dimensions as follows: Height = 110 cm, Depth =
25 cm, Breadth = 85 cm (see figure). The thickness of
the 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.​

Answer 1

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

$\huge{\boxed{\bf{\red{₹6275}}}}$

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

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

__________________________

Answer 2

External length (l)(l) of bookshelf=85cm85cm

External breadth (b)(b) of bookshelf=25cm25cm

External height (h)(h) of bookshelf=110cm110cm

External surface area of book shelf while leaving out the front face of the shelf

=lh+2(lb+bh)lh+2(lb+bh)

=(85×110)+2(85×25+25×110)(85×110)+2(85×25+25×110)

=9350+97509350+9750

=19100cm^219100cm²

Area of front face

=(85×110)−75×100+2(75×5)(85×110)−75×100+2(75×5)

=1850+760=2600cm^21850+760=2600²

Area to be polished

=19100+260019100+2600

=21700cm^221700cm ²

Cost of polishing

= ₹21700×0.20₹21700×0.20

= ₹4340₹4340

Length, breadth and height of each row of bookshelf are

75cm,20cm and 30 cm.75cm,20cmand30cm.

From the figure Area to be painted in 1 row

=2(l+h)b+lh2(l+h)b+lh

=2(75+30)20+75×302(75+30)20+75×30

=6450cm^26450cm²

Area to be painted in 3 rows

= 3×6450=19350cm^23×6450=19350cm ²

Total cost of painting

=₹(19350×0.1)=₹ 1935₹(19350×0.1)=₹1935

Total expenses

=₹(4340+1935)

=₹6275₹(4340+1935)=₹6275