NCERT Class 9 Maths Solutions Chapter - 13 Surface Areas and Volumes, Ex - 13.9

Ex -13.9

Question 1.  A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm. 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.


Solution

 External length (l) of bookshelf = 85 cm
    External breadth (b) of bookshelf = 25 cm
    External height (h) of bookshelf = 110 cm
    External surface area of shelf while leaving front face of shelf
                                                  = lh + 2 (lb + bh)
                                                  = [85  110 + 2 (85  25 + 25  110)] cm²
                                                  = 19100 cm²
    Area of front face = [85  110 - 75  100 + 2 (75  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  0.20) = Rs 4340  
  
    Now, length (l), breadth (b) height (h) of each row of bookshelf is 75 cm, 20 cm, and

    30cm  respectively.
    Area to be painted in 1 row = 2 (l + h) b + lh
                                           = [2 (75 + 30)  20 + 75  30] cm²
                                           = (4200 + 2250) cm²
                                           = 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  0.10) = Rs 1935  
    Total expense required for polishing and painting the surface of the bookshelf 

                                            = Rs(4340 + 1935) = Rs 6275

Question 2.  The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm² and black paint costs 5 paise per cm².

Solution

Radius (r) of a wooden sphere = 

Surface area of a wooden sphere = =
  
Radius (r') of cylindrical support = 1.5 cm
Height (h) of cylindrical support = 7 cm

CSA of cylindrical support = 2r'h

                                    
Area of circular end of cylindrical support = r² 

                                                         

                                                           = 7.07 cm²
Area to be painted silver = [8  (1386 - 7.07)] cm²
                                       = (8  1378.93) cm² = 11031.44 cm²
Cost occurred in painting silver colour = Rs (11031.44  0.25) = Rs 2757.86  

Area to painted black = (8  66) cm² = 528 cm²
Cost occurred in painting black colour = Rs (528  0.05) = Rs 26.40
Total cost occurred in painting = Rs (2757.86 + 26.40) = Rs 2784.26

Question 3.  The diameter of a sphere is decreased by 25%. By what per cent does its curved surface area decrease?

Solution

Let the diameter of the sphere be d.
Radius (r₁) of the sphere = 
It is given that the diameter of the sphere is decreased by 25%.
 New radus (r₂) of the sphere = 

CSA (S₁) of the sphere =    
CSA (S₂) of the new sphere =  
Decrease in CSA of sphere = S₁ - S₂  
     
Percentage decrease in CSA of sphere= 

                                                      %

Ex-13.8

Ex-14.1