NCERT Class 9 Maths Solutions Chapter - 13 Surface Areas and Volumes, Ex - 13.7

Ex - 13.7

Question 1.  Assume  , unless stated otherwise.
Find the volume of the right circular cone with
(i)    radius 6 cm, height 7 cm
(ii)   radius 3.5 cm, height 12 cm

Solution

(i)    Radius (r) of cone = 6 cm
       Height (h) of cone = 7 cm
       Volume of cone   

(ii)   Radius (r) of cone = 3.5 cm
       Height (h) of cone = 12 cm
       Volume of cone  

Question 2.  Assume , unless stated otherwise
Find the capacity in litres of a conical vessel with
(i)    radius 7 cm, slant height 25 cm
(ii)   height 12 cm, slant height 13 cm

Solution

(i)    Radius (r) of cone = 7 cm
       Slant height (l) of cone = 25 cm
       Height (h) of cone   
       Volume of cone  
       Capacity of the conical vessel =  litres= 1.232 litres

(ii)    Height (h) of cone = 12 cm
        Slant height (l) of cone = 13 cm
        Radius (r) of cone 
        Volume of cone   
        Capacity of the conical vessel = litres =  litres.

Question 3.  The height of a cone is 15 cm. If its volume is 1570 cm³, find the diameter of its base.(Use  = 3.14)

Solution

Height (h) of cone = 15 cm
Let radius of cone be r.
Volume of cone = 1570 cm³
 

 

 r = 10 cm

Thus, the radius of the base of the cone is 10 cm.

Question 4.  Assume  , unless stated otherwise. 

If the volume of a right circular cone of height 9 cm is 48 cm³, find the diameter of its base.

Solution

 Height (h) of cone = 9 cm
   Let radius of cone be r.
   Volume of cone = 48 cm3

   

  Thus, the diameter of the base of the cone is 2r = 8 cm.

Question 5.  Assume , unless stated otherwise

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

Solution

Radius (r) of pit =
Depth (h) of pit = 12 m
Volume of pit =  = 38.5 m³

Capacity of the pit = (38.5  1) kilolitres = 38.5 kilolitres

Question 6.  Assume  , unless stated otherwise.

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find

(i)    height of the cone

(ii)    slant height of the cone

(iii)   curved surface area of the cone

Solution

(i)    Radius of cone =   =14 cm
       Let height of cone be h.
       Volume of cone = 9856 cm³
       

       h = 48 cm

       Thus, the height of the cone is 48 cm.

(ii)   Slant height (l) of cone  

            
       Thus, the slant height of the cone is 50 cm.

(iii)    CSA of cone = rl=   = 2200 cm²

^{Question 7.}  Assume , unless stated otherwise.

A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

Solution

When the right angled ABC is revolved about its side 12 cm, a cone of height (h) 12 cm, radius (r) 5 cm, and slant height (l) 13 cm will be formed.    
Volume of cone    = 100 cm³
Thus, the volume of cone so formed by the triangle is 100 cm³.

Question 8.  Assume , unless stated otherwise.

If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

Solution

When the right angled ABC is revolved about its side 5 cm, a cone of radius (r) 12 cm, height (h) 5 cm, and slant height (l) 13 cm will be formed.
  
Volume of cone = 

Required ratio  

Question 9.  Assume , unless stated otherwise.

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

Solution

Radius (r) of heap
Height (h) of heap = 3 m
Volume of heap=  
Slant height (l) =

Area of canvas required = CSA of cone

    

Ex-13.6

Ex-13.8