Question

$\huge \underline{ \rm{Math \: Question:-}}$
A wooden blockshelf has external dimensions as follow:Height=110cm,Depth=25cm,Breadth=85cm (see attached figure).The thickness of the plank is 5cm everywhere. The external faces are to be polished and the inner faces are to be painted.If the rate of polishing is 30 paise per cm² and the rate of painting is 20 paise per cm².Find the total expenses required for polishing and painting the surface of the bookshelf.

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Answer 1

Given :

• Length, l = 85cm
• Breadth, b = 25cm
• Hieght, h = 110cm

To find :

• Find the total expenses required for polishing and painting the surface of the bookshelf ?

Solution :

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

Surface area to be polished

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

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

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

$:\implies{\underline{\boxed{\frak{\pink{21700\:cm^{2}}}}}}$★

$∴$ Expenses required for polishing @ 20 paise per cm²

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

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

⠀⠀⠀⠀⠀⠀⠀⠀$:\implies{\underline{\boxed{\frak{\pink{₹\:4340}}}}}$★

Surface area to be painted

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

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

$:\implies{\underline{\boxed{\frak{\pink{19350\:cm^{2}}}}}}$★

$∴$ Expenses required for painting @ 10 paise per cm²

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

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

⠀⠀⠀⠀⠀⠀⠀⠀$:\implies{\underline{\boxed{\frak{\pink{₹\:1935}}}}}$★

$∴$Total expenses required for polishing and painting the surface of the bookshelf

$:\implies{\sf{₹\:4340\:+\:₹\:1935}}$

$:\implies{\underline{\boxed{\frak{\pink{₹\:6275}}}}}$★

$∴$Hence,

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

Answer 2

External dimensions of book self,

⟹ Length , I = 85 cm

⟹ Breadth,b = 25 cm

⟹ Height, h = 110 cm

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

$\sf{ = lh + 2(lb + bh)}=lh+2(lb+bh)$

$\sf{=[85×110+2(85×25+25×110)]}$

$\sf{=(9350+9750)}$

$\sf{=19100}=$

External surface area of shelf is $\bf{19100\:\:{cm}^{2}}$

Area of front face,

$\sf{=[85×110-75×100+2(75×5)]}$

$\sf{=1850+750}$

$\sf{=2600}$

So,area is $\bf{2600\:\:{cm}^{2}}$

• Area to be polished,

$\sf{(19100+2600)\:\:{cm}^{2}}$

$\sf{=21700\:\:{cm}{2}}$

Cost of polishing 1 cm² area = Rs 0.20

So,Cost of polishing 2700 cm² area =Rs (21700×0.20)

=Rs 4340

Dimensions of row of the book shelf

Length (l) = 75 cm

Breadth (b) = 20 cm

Height (h) = 30 cm

Area to be painted in one row,

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

$= 2(75 + 30) \times 20 + 75 \times 30=2(75+30)×20+75×30$

= 4200 + 2250=4200+2250

= 6450=6450

So,area is $\bf{6450\:\:{cm}^{2}}$

Area to be painted in 3 rows,

= $(3 \times 6450) \: \: {cm}^{2}$

= $→19350 \: \: {cm}^{2}$

✵Cost of painting 1 cm² area = Rs 0.10✵

So, Cost of painting 19350 cm² = Rs (19350×0.1)

=Rs. 1935

⟹ Total expenses required for polishing and painting = Rs.(4340+1935) = Rs.6275

✯$\large{ \underline{ \overline{ \mid{ \rm{ \red{Answer→ Rs\:6275}} \mid}}}}$✯