Question

A wooden bookshelf has external dimensions as follows: Height = 110cm, Depth = 25cm,

Breadth = 85cm (see fig. 13.31). 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 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

Answer ⤵️

ANSWER

External length (l) of bookshelf=85㎝

External breadth (b) of bookshelf=25㎝

External height (h) of bookshelf=110㎝

External surface area of book shelf while leaving out the front face of the shelf=lh+2(lb+bh)

=(85×110)+2(85×25+25×110)

=9350+9750

=19100㎠

Area if front face=(85×110)−75×100+2(75×5)

=1850+760=2600㎠

Area to be polished=19100+2600=21700㎠

Cost of polishing=Rs. 21700×0.20=Rs.4340

Length, breadth and height of each row of bookshelf are

75㎝,20㎝ & 30㎝ respectively. From the figure Area to be painted in 1 row=2(l+h)b+lh

=2(75+30)20+75×30

=6450㎠

Area to be painted in 3 rows=3×6450=19350㎠

Total cost of painting=Rs.(19350×0.1)=Rs. 1935

Total expenses=Rs.(4340+1935)=Rs. 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

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

$\sf{=[85×110+2(85×25+25×110)]}$

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

$\sf{=19100}$

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,

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

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

$= 4200 + 2250$

$= 6450$

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

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