Solution: 

External height (l) of book self = 85 cm

External breadth (b) of book self = 25 cm

External height (h) of book self = 110 cm

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

= lh + 2 (lb + bh)

= [85 x 110 + 2 (85 x 25 + 25 x 110)] cm²

= (9350 + 9750) cm²

= 19100 cm²

Area of front face = [85 x 110 - 75 x 100 + 2 (75 x 5)] cm²

= 1850 + 750 cm²

= 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 x 0.20) = Rs 4340

 

It can be observed that length (l), breadth (b), and height (h) of each row of the book shelf is 75 cm, 20 cm, and 30 cm respectively.

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

= [2 (75 + 30) x 20 + 75 x 30] cm²

= (4200 + 2250) cm²

= 6450 cm²

Area to be painted in 3 rows = (3 x 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

Therefore, it will cost Rs 6275 for polishing and painting the surface of the bookshelf.

Solution: 

 

Radius (r) of wooden sphere = 21/2 cm = 10.5 cm
Surface area of wooden sphere = 4πr² 

Radius (r₁) of the circular end of cylindrical support = 1.5 cm

Height (h) of cylindrical support = 7 cm

CSA of cylindrical support = 2πrh

= 7.07 cm²

Area to be painted silver = [8 × (1386 - 7.07)] cm²

= (8 × 1378.93) cm² = 11031.44 cm²

Cost for painting with silver colour = Rs (11031.44 × 0.25) = Rs 2757.86

Area to be painted black = (8 × 66) cm² = 528 cm²

Cost for painting with black colour = Rs (528 × 0.05) = Rs 26.40

Total cost in painting = Rs (2757.86 + 26.40)

= Rs 2784.26

Therefore, it will cost Rs 2784.26 in painting in such a way.

 

Let the diameter of the sphere be d.