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Q : 9    A heap of wheat is in the form of a cone whose diameter is \small 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.
 

Given, Height of the conical heap =   Base radius of the cone =  We know,  The volume of a cone =  The required volume of the cone formed =  Now, The slant height of the cone =  We know, the curved surface area of a cone =  The required area of the canvas to cover the heap  =   

7. 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

Q : 8    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.
 

When a right-angled triangle is revolved about the perpendicular side, a cone is formed whose, Height of the cone = Length of the axis=  Base radius of the cone =  And, Slant height of the cone =  We know,  The volume of a cone =  The required volume of the cone formed =  Now, Ratio of the volumes of the two solids =  Therefore, the required ratio is 

Q : 7    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.
 

When a right-angled triangle is revolved about the perpendicular side, a cone is formed whose, Height of the cone = Length of the axis=  Base radius of the cone =  And, Slant height of the cone =  We know,  The volume of a cone =  The required volume of the cone formed =  Therefore, the volume of the solid cone obtained is 

Q : 7    The volume of a right circular cone is \small 9856\hspace{1mm}cm^3. If the diameter of the base is 28 cm, find

             (iii) curved surface area of the cone
 

Given, a right circular cone. The radius of the base of the cone =  And Slant height of the cone =   (iii) We know, The curved surface area of a cone =  Required curved surface area= 

Q : 6    The volume of a right circular cone is \small 9856\hspace{1mm}cm^3. If the diameter of the base is 28 cm, find

            (ii) slant height of the cone 
 

Given, a right circular cone. The volume of the cone =  The radius of the base of the cone =  And the height of the cone =   (ii) We know, Slant height,  Therefore, the slant height of the cone is 

Q : 6    The volume of a right circular cone is \small 9856\hspace{1mm}cm^3. If the diameter of the base is 28 cm, find

            (i) height of the cone

Given, a right circular cone. The radius of the base of the cone =  The volume of the cone =  (i) Let the height of the cone be  We know, The volume of a right circular cone =      Therefore, the height of the cone is   

Q : 5    A conical pit of top diameter \small 3.5 m is 12 m deep. What is its capacity in kilolitres?

Given, Depth of the conical pit  =  The top radius of the conical pit =  We know, The volume of a right circular cone =   The volume of the conical pit =    Now,   The capacity of the pit =   

Q : 4    If the volume of a right circular cone of height 9 cm is \small 48\pi \hspace{1mm}cm^3, find the diameter of its base.
 

Given, Height of the cone =  Let the radius of the base of the cone be  We know, The volume of a right circular cone =    Therefore the diameter of the right circular cone is 

Q : 3    The height of a cone is 15 cm. If its volume is 1570 \small cm^3, find the radius of the base. (Use \small \pi =3.14

Given, Height of the cone =  Let the radius of the base of the cone be  We know, The volume of a right circular cone =   

Q : 2     Find the capacity in litres of a conical vessel with

             (ii) height 12 cm, slant height 13 cm 

Given, Height =  Slant height =  Radius =  We know, Volume of a right circular cone =   Volume of the vessel=   Required capacity of the vessel = 

Q : 2     Find the capacity in litres of a conical vessel with

            (i) radius 7 cm, slant height 25 cm

Given, Radius =  Slant height =  Height =  We know, Volume of a right circular cone =   Volume of the vessel=   Required capacity of the vessel = 

Q: 1    Find the volume of the right circular cone with:

            (ii) radius \small 3.5 cm, height 12 cm

Given, Radius =  Height =  We know, Volume of a right circular cone =   Required volume = 

Q : 1    Find the volume of the right circular cone with

            (i) radius 6 cm, height 7 cm

Given, Radius =  Height =  We know, Volume of a right circular cone =   Required volume =   

Q: 8    A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

Given, Height =  The radius of the cylindrical bowl  =   The volume of soup in a bowl for a single person =   The volume of soup given for 250 patients = Therefore, the amount of soup the hospital has to prepare daily to serve 250 patients is 

Q : 7     A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

Given, Length of the cylindrical pencil =  The radius of the graphite (Inner solid cylinder)  =  Radius of the pencil (Inner solid graphite cylinder + Hollow wooden cylinder) = =  We know, Volume of a cylinder=   The volume of graphite =  And, Volume of wood =  Therefore, the volume of wood is  and the volume of graphite is 

Q : 6     The capacity of a closed cylindrical vessel of height 1 m is \small 15.4 litres. How many square metres of metal sheet would be needed to make it?
 

(Using capacity(volume), we will find the radius and then find the surface area) The capacity of the vessel = Volume of the vessel = litres Height of the cylindrical vessel =  Let the radius of the circular base be   The volume of the cylindrical vessel =  Therefore, the total surface area of the vessel =  Therefore, square metres of metal sheet needed to make it is  

Q : 5    It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per \small m^2, find

             (iii) capacity of the vessel.

(iii) Height of the cylinder =  Radius of the base of the vessel =    Volume of the cylindrical vessel =  Therefore, the capacity of the cylindrical vessel is 

Q : 5    It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per \small m^2, find

            (ii) radius of the base.

The inner curved surface area of the cylindrical vessel =  Height of the cylinder =  Let the radius of the circular base be   The inner curved surface area of the cylindrical vessel =  Therefore, the radius of the base of the vessel is 

Q : 5    It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per \small m^2, find

(i) inner curved surface area of the vessel,

(i) Given, Rs 20 is the cost of painting  area of the inner curved surface of the cylinder.   Rs 2200 is the cost of painting area of the inner curved surface of the cylinder.   The inner curved surface area of the cylindrical vessel = 

Q : 4    If the lateral surface of a cylinder is \small 94.2\hspace{1mm}cm^2 and its height is 5 cm, then find

            (ii) it's volume. (Use \small \pi =3.14)
 

Given, The lateral surface area of the cylinder =  Height of the cylinder =  The radius of the base is  (ii) We know, The volume of a cylinder =  Therefore, volume of the cylinder is 
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