A wooden bookshelf has external dimensions as follows: Height = 110cm, Depth = 25cm, Breadth = 85 cm (see fig.). 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.
External dimensions of book self,
Length, l = 85cm
Breadth, b = 25 cm
Height, h = 110 cm
External surface area of shelf while leaving out the front face of the shelf
= lh + 2(lb + bh)
= [85 × 110 + 2(85 × 25 + 25 × 110)]
= (9350 + 9750)
= 19100
External surface area of shelf is 19100 cm2
Area of front face = [85 × 110 - 75 × 100 + 2(75 × 5)]
= 1850 + 750
So, area is 2600 cm2
Area to be polished = (19100 + 2600) cm2
= 21700 cm2.
Cost of polishing 1 cm2 area = Rs 0.20
Cost of polishing 21700 cm2 area Rs. (21700 × 0.20)
= Rs 4340
Dimensions of row of the book shelf
Length(l) = 75 cm
Breadth (b) = 20 cm and
Height(h) = 30 cm
Area to be painted in one row= 2(l + h)b + lh
= [2(75 + 30) × 20 + 75 × 30]
= (4200 + 2250) = 6450
So, area is 6450 cm2.
Area to be painted in 3 rows = (3 × 6450)cm2
= 19350 cm2.
Cost of painting 1 cm2 area = Rs. 0.10
Cost of painting 19350 cm2 area = Rs (19350 x 0.1)
= Rs 1935
Total expense required for polishing and painting = Rs. (4340 + 1935)
= Rs. 6275
The cost for polishing and painting the surface of the book shelf is Rs. 6275.