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

Solution:

External length of book shelf = 85 cm

Breadth = 25 cm

Height = 110 cm

External surface area of shelf while leaving front face of shelf

lh + 2(lb + bh)

[85 * 110 + 2(85 * 25 + 25 * 110)]

$19100 \mathrm{~cm}^{2}$

Area of Front face $=\left[85^{*} 110-75^{*} 100+2\left(75^{*} 5\right)\right] \mathrm{cm}^{2}$

$=1850+750 \mathrm{~cm}^{2}$

$=2600 \mathrm{~cm}^{2}$

Area to be polished $=19100+2600 \mathrm{~cm}^{2}$

$=21700 \mathrm{~cm}^{2}$

Cost of polishing $1 \mathrm{~cm}^{2}$ area $=$ Rs. $0.20$

Cost of polishing $21700 \mathrm{~cm}^{2}$ area $=21700 * 0.20$

= Rs. 4340

Now, Length (l), breadth (b), height ( $h$ ) of each row of book shelf is $75 \mathrm{~cm}, 20 \mathrm{~cm}$ and $30 \mathrm{~cm}=\left(\frac{110-20}{3}\right)$

respectively.

Area to be painted in 1 row = 2(l + h)b + lh

$[2(75+30) * 20+75 * 30)] \mathrm{cm}^{2}$

$(4200+2250) \mathrm{cm}^{2}$

$6450 \mathrm{~cm}^{2}$

Area to be painted in 3 rows = 3 * 6450

$=$ Rs. $19350 \mathrm{~cm}^{2}$

Cost of painting $1 \mathrm{~cm}^{2}$ area $=$ Rs. $0.10$

Cost of painting $19350 \mathrm{~cm}^{2}$ area $=19350 * 0.10$

= Rs.1935

Total expense required for polishing and painting the surface of the bookshelf = 4340 + 1935

= Rs.6275