NCERT Class 9 Maths Solutions Chapter - 13 Surface Areas and Volumes, Ex - 13.2

Ex -13.2

Question 1.  Assume  ,  unless stated otherwise
The curved surface area of a right circular cylinder of height 14 cm is 88 . Find the diameter of the base of the cylinder.

Solution

Height of the cylinder = 14 cm 
    Let diameter of cylinder be d and the radius of its base be r.
    Curved surface area of cylinder = 88 
     
    
     
      
Thus, the diameter of the base of the cylinder is 2 cm.

Question 2.  Assume , unless started otherwise.
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?

Solution

Height (h) of cylindrical tank = 1 m.
    Base radius (r) of cylindrical tank =  = 70 cm = 0.7 m

Area of sheet required = total surface area of tank = 

   

So, it will require 7.48 area of sheet.

Question 3.  A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find its

(i)    Inner curved surface area,

(ii)   Outer curved surface area,

(iii)   Total surface area.

Solution

Inner radius  of cylindrical pipe = 2 cm
 Outer radius  of cylindrical pipe = 2.2 cm
 Height (h) of cylindrical pipe = length of cylindrical pipe = 77 cm
  
(i) CSA of inner surface of pipe = 

(ii) CSA of outer surface of pipe = 

=     

=      

= 1064.8 

(iii) Total surface area of pipe =    

CSA of inner surface + CSA of outer surface+ area of both circular ends of pipe

Thus, the total surface area of cylindrical pipe is 2038.08 .

Question 4.  Assume , unless started otherwise

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in ?

Solution

The roller is cylindrical.
Height of the roller = length of roller = 120 cm
Radius of the circular end of the roller =  
CSA of roller = 
Area of field = 500  CSA of roller = (500 31680) = 15840000 
    = 1584 

Question 5.  Assume , unless started otherwise

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs.12.50 per .

Solution

Height of the pillar = 3.5 m
Radius of the circular end of the pillar = cm = 25 cm  = 0.25 m
CSA of pillar =  = 
Cost of painting 1  area = Rs 12.50
Cost of painting 5.5  area = Rs (5.5 12.50) = Rs 68.75

Thus, the cost of painting the CSA of pillar is Rs 68.75.

Question 6.  Assume , unless started otherwise

Curved surface area of a right circular cylinder is 4.4 . If the radius of the base of the cylinder is 0.7 m, find its height.

Solution

  Let the height of the cylinder be h.
Radius of the base of the cylinder = 0.7 m
    CSA of cylinder = 4.4 
     = 4.4 

    
    h = 1 m
    Thus, the height of the cylinder is 1 m.

Question 7.  Assume , unless started otherwise

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find

(i)    Its inner curved surface area,

(ii)    The cost of plastering this curved surface at the rate of Rs 40 per 

Solution

Inner radius (r) of circular well
Depth (h) of circular well = 10 m 

(i) Inner curved surface area = 

                                      
                            = (44  0.25  10) 
            = 110 
  
    (ii) Cost of plastering 1  area = Rs 40                  
    Cost of plastering 110  area = Rs (110  40) = Rs 4400

Question 8.  Assume , unless stated otherwise.

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.

Solution

 Height (h) of cylindrical pipe = Length of cylindrical pipe = 28 m
  Radius (r) of circular end of pipe =  cm = 2.5 cm = 0.025 m
  CSA of cylindrical pipe =   = 4.4 
    Thus, the area of radiating surface of the system is 4.4 .

Question 9.  Assume , unless stated otherwise.

Find

(i)  the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.

(ii)  how much steel was actually used, if  of the steel actually used was wasted in making the tank.

Solution

Height (h) cylindrical tank = 4.5 m
    Radius (r) of circular end of cylindrical tank =m = 2.1m
    (i)    Lateral or curved surface area of tank = 

                                    =                                         
                                    = 59.4 m²          
  
    (ii)    Total surface area of tank = 2 (r + h)

              =                            
              = 87.12 m²

    Let A m² steel sheet be actually used in making the tank.

Thus, 95.04  steel was used in actual while making the tank.

Question 10.  Assume , unless started otherwise

In the given figure, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.

Solution

    Height of frame of lampshade = (2.5 + 30 + 2.5) cm = 35 cm
    Radius of the circular end of frame of lampshade = cm = 10cm
    Cloth required for covering the lampshade = 

                                                                
                                = 2200 
  
     Thus, for covering the lampshade 2200  cloth will be required.

Question 11.  Assume , unless started otherwise

The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

Solution

Radius of circular end of cylindrical penholder = 3 cm
Height of penholder = 10.5 cm
Surface area of 1 penholder = CSA of penholder + Area of base of     

penholder =  + 

                  
Area of cardboard sheet used by 1 competitor =  
    Area of cardboard sheet used by 35 competitors

 = 7920 cm²
    Thus, 7920  cardboard sheet will be bought for the competition.

Ex-13.1

Ex-13.3