Question

A wooden bookshelf has external

dimensions as follows: Height = 110
cm, Depth = 25 cm, Breadth = 85 cm
(See Figure). The thickness of the plank
is 5 cm every where. 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.

(i) Find the volume of the bookshelf.

(ii) Find the external surface area.

(iii) Find the internal surface area of one

row.

(iv) Find the total expenses required for

polishing and painting the surface of the

bookshelf.​​

Answer 1

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