# A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see Fig. 13.31). 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 cm^{2} and the rate of painting is 10 paise per cm^{2}, find the total expenses required for polishing and painting the surface of the bookshelf.

**Solution:**

Since the bookshelf is cuboidal in shape and opened at the front with three shelves of the same dimensions, the area to be polished will be 5 surfaces of cuboidal bookshelf and the front border with plank’s thickness.

The area to be painted will be 3 shelves of the bookshelf with internal dimensions and the area of each shelf will be 5 surfaces of the cuboidal shelf.

We can calculate the total cost of polishing and painting by multiplying the rate and their respective area.

The Volume of a cuboid of length l, breadth b, and height h, is = l × b × h

External measures of the bookshelf is,

Breadth, B = 85 cm

Depth, D = 25 cm

Height, H = 110 cm

The thickness of the plank, t = 5 cm

Internal measures of the bookshelf is,

The breadth of each shelf, b = B - 2t

⇒ b = 85 cm - 2 × 5 cm = 75 cm

Depth of each shelf, d = D - t

⇒ d = 25 cm - 5 cm = 20 cm

Height of each shelf, h = H - 4t

= (110 cm - 4 × 5 cm) ÷ 3

= 90 cm / 3 = 30 cm

Now, Surface area to be polished = External 5 surfaces of the bookshelf + border of the shelf

= 2(B + H) D + BH + 2Ht + 4bt

= [2 × (85 cm + 110 cm) × 25 cm] + (85 cm × 110 cm) + (2 × 110 cm × 5 cm) + (4 × 75 cm × 5 cm)

= 9750 cm^{2} + 9350 cm^{2} + 1100 cm^{2} + 1500 cm^{2}

= 21700 cm^{2}

Cost of polishing at the rate of 20 paise per cm^{2} = 21700 cm^{2} × (₹ 20/100) / cm^{2} = ₹ 4340

Surface area to be painted = Internal 5 surfaces of 3 shelves

= 3 [2(b + h)d + bh]

= 3 [2 × (75 cm + 30 cm) × 20 cm + (75 cm × 30 cm)]

= 3 [4200cm^{2} + 2250 cm^{2}]

= 3 × 6450 cm^{2}

= 19350 cm^{2}

Cost of painting at the rate of 10 paise per cm^{2} = 19350 cm^{2} × (₹ 10/100) / cm^{2} = ₹ 1935

Total expense required for polishing and painting = ₹ 4340 + ₹ 1935 = ₹ 6275

Thus, the total expense required for polishing and painting the surface of the bookshelf is ₹ 6275.

**Video Solution:**

## A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see Fig. 13.31). 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.

### NCERT Solutions for Class 9 Maths - Chapter 13 Exercise 13.9 Question 1:

**Summary:**

It is given that the wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm with the thickness of the plank as 5 cm everywhere. If the external faces are to be polished and the inner faces are to be painted given the rate of polishing is 20 paise per cm² and the rate of painting is 10 paise per cm², we have found that the total expense required for polishing and painting the surface of the bookshelf is ₹ 6275.