NCERT Class 9 Maths Solutions Chapter - 13 Surface Areas and Volumes, Ex - 13.3

Ex - 13.3

Question 1.  Assume , unless started otherwise
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Solution

Radius of base of cone = cm = 5.25 cm
Slant height of cone = 10 cm
CSA of cone =  = 
Thus, the curved surface area of cone is 165 .

Question 2.  Assume , unless stated otherwise.
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

Solution

Radius of base of cone = m = 12 cm
Slant height of cone = 21 m
Total surface area of cone = (r + l)

Question 3.  Assume  , unless stated otherwise.

Curved surface area of a cone is 308  and its slant height is 14 cm.     

Find

(i)    radius of the base and     (ii)    total surface area of the cone.

Solution

(i)    Slant height of cone = 14 cm
    Let radius of circular end of cone be r.
    CSA of cone = 

    
    Thus, the radius of circular end of the cone is 7 cm.

(ii)    Total surface area of cone = CSA of cone + Area of base
                     =

Thus, the total surface area of the cone is 462 .

Question 4.  Assume  , unless stated otherwise.

A conical tent is 10 m high and the radius of its base is 24 m. Find

(i)    Slant height of the tent

(ii)    Cost of the canvas required to make the tent, if the cost of 1  canvas is Rs 70.

Solution

(i)    Height (h) of conical tent = 10 m
        Radius (r) of conical tent = 24 m
        Let slant height of conical tent be l.
           

          l = 26 m

.

        Thus, the slant height of the conical tent is 26 m.

    (ii)    CSA of tent =  = 
        Cost of 1  canvas = Rs 70
        Cost of  canvas =  = Rs 137280
        Thus, the cost of canvas required to make the tent is Rs 137280.

Question 5.  Assume , unless stated otherwise.

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use  = 3.14).

Solution

Height (h) of conical tent = 8 m
    Radius (r) of base of tent = 6 m
    Slant height (l) of tent =      
    CSA of conical tent =  = (3.14  6  10)  = 188.4 

Let length of tarpaulin sheet required be L. 
As 20 cm will be wasted so, effective length will be (L - 0.2 m) 
Breadth of tarpaulin = 3 m 
Area of sheet = CSA of tent 
    [(L - 0.2 m)  3] m = 188.4 
    L - 0.2 m = 62.8 m
    L = 63 m
    
    Thus, the length of the tarpaulin sheet will be 63 m.

Question 6.  Assume , unless stated otherwise.

The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 .

Solution

Slant height (l) of conical tomb = 25 m
    Base radius (r) of tomb = = 7 m
    CSA of conical tomb =  =  
    Cost of white-washing 100  area = Rs 210
    Cost of white-washing 550  area =Rs = Rs 1155
    Thus, the cost of white washing the conical tomb is Rs 1155.

Question 7.  Assume , unless stated otherwise.

A joker's cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

Solution

Radius (r) of conical cap = 7 cm
    Height (h) of conical cap = 24 cm
    Slant height (l) of conical cap =  
    CSA of 1 conical cap = =  
    CSA of 10 such conical caps = (10  550)  = 5500 
    
    Thus, 5500  sheet will be required to make the 10 caps.

Question 8.  Assume , unless stated otherwise.

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. if the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per , what will be the cost of painting all these cones? (Use  = 3.14 and take = 1.02).

Solution

Radius (r) of cone =  = 0.2 m
    Height (h) of cone = 1 m

    Slant height (l) of cone = 
    CSA of each cone =  = (3.14  0.2  1.02)  = 0.64056   
    CSA of 50 such cones = (50  0.64056)  = 32.028   
  
    Cost of painting 1  area = Rs 12
    Cost of painting 32.028  area = Rs (32.028  12) = Rs 384.336
   
    Thus, it will cost Rs 384.34 (approximately) in painting the 50 hollow cones.

Ex-13.2

Ex-13.4