Question

A wooden bookshelf has external dimensions as follows : Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (See Fig. 18.5). The thickness of the plank is 5 cm 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

The total expenses required for polishing and painting the surface of the bookshelf is Rs. 6275.

The calculations are fully based on the given diagram.

Refer to the diagram every time while going through each step.

Let "l" be the length of open shelf

Let "h" be the height of open shelf

From given data, we have,

Height = 110 cm, Depth = 25 cm, Breadth = 85 cm.

The thickness of the plank is 5 cm everywhere.

Height of the book shelf = 3 × height of open portion + 4 × thickness of the plank

110 = 3h + 4 × 5

110 = 3h + 20

3h = 90

h = 90/3 = 30 cm

Length of book shelf = Length of open portion + 2 × thickness of the plank

85 = l + 2 × 5

85 = l + 10

l = 75 cm

Area of book shelf to be polished = TSA of external book shelf - 3 × Area of open portion

= 2 (85 × 25 + 25 × 110 + 110 × 85) - 3 (75 × 30)

= 2 (14225) - 3 (2250)

= 28450 - 6750

= 21700 cm^2

Cost of polishing 1 cm^2 = 20 paise

Cost of polishing 21700 cm^2 = 20 paise × 21700 = 434000 paise

= Rs. 4340

Inner surface need to be painted

Total area to be painted = 3 × (TSA of internal of shelf - Area of open portion)

= 3 × (2 (30 × 75 + 75 × 20 + 20 × 30) - (30 × 75))

= 3 × (2 (4350) - 2250)

= 3 × 6450

= 19350 cm^2

Cost of painting 1 cm^2 = 10 paise

Cost of painting 19350 cm^2 = 10 paise × 19350 = 193500 paise

= Rs. 1935

Total expenses = Cost of polishing + Cost of painting

= 4340 + 1935

=  Rs. 6275

Answer 2

$\huge\bold\green{Solution:}$

External length $(l)$ of bookshelf=$85cm$

External breadth $(b)$ of bookshelf=$25cm$

External height $(h)$ of bookshelf=$110cm$

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

=$lh+2(lb+bh)$

=$(85×110)+2(85×25+25×110)$

=$9350+9750$

=$19100cm^2$

Area of front face

=$(85×110)−75×100+2(75×5)$

=$1850+760=2600cm^2$

Area to be polished

=$19100+2600$

=$21700cm^2$

Cost of polishing

= $₹\:21700×0.20$

= $₹4340$

Length, breadth and height of each row of bookshelf are

$75cm,20cm\: and \:30 cm.$

From the figure Area to be painted in 1 row

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

=$2(75+30)20+75×30$

=$6450cm^2$

Area to be painted in 3 rows

= $3×6450=19350cm^2$

Total cost of painting

=$₹(19350×0.1)=₹ 1935$

Total expenses

=$₹(4340+1935)=₹\:6275$