07 - Question bank -Surface Area and Volume - Class 10 - Maths Class 10 Notes | EduRev

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Class 10 : 07 - Question bank -Surface Area and Volume - Class 10 - Maths Class 10 Notes | EduRev

 Page 1


Surface and volume of cube, cuboid, and cylinder 
 
Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per 
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. 
Given: For Cuboidal Room, 
            Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m 
            To find  cost of painting four walls we first need to find the surface area of four walls . 
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h 
 
 
 
     Vertical surface area of cuboid=180 m
2
. 
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting                                                                  
       =180×13 
                                                             =2340  
Therefore Cost of Painting the four wall is 2340 Rs 
 
Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what 
will be the weight of the pillar. 
Given: For Pillar [cuboid] 
            Length =600cm= 
600
100
=6m 
         Breadth =55cm= 
55
100
=0.55m 
           Height=25cm= 
25
100
=0.25m 
 
=2(10+5)×6 
 =2(15)×6 
=180 
 
                            
                            
l 
h 
b 
Tip: Remember to convert 
dimensions from cm to m as 
weight per cube is given in m
3 
Page 2


Surface and volume of cube, cuboid, and cylinder 
 
Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per 
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. 
Given: For Cuboidal Room, 
            Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m 
            To find  cost of painting four walls we first need to find the surface area of four walls . 
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h 
 
 
 
     Vertical surface area of cuboid=180 m
2
. 
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting                                                                  
       =180×13 
                                                             =2340  
Therefore Cost of Painting the four wall is 2340 Rs 
 
Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what 
will be the weight of the pillar. 
Given: For Pillar [cuboid] 
            Length =600cm= 
600
100
=6m 
         Breadth =55cm= 
55
100
=0.55m 
           Height=25cm= 
25
100
=0.25m 
 
=2(10+5)×6 
 =2(15)×6 
=180 
 
                            
                            
l 
h 
b 
Tip: Remember to convert 
dimensions from cm to m as 
weight per cube is given in m
3 
Solution 
Volume of Beam pillar[cuboid]= ?? × ?? × h 
                                                          =6×0.55×0.25 
                                                          =0.825 m
3
 
Weight of pillar=Volume of pillar×weight of volume per m
3
 
                               =0.825×200 
                                =165 Kg 
Weight of pillar=165 Kg        
 
Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a 
playground. Find the area of playground in m
2
.  
Solution: The Diameter cylindrical roller =40 cm 
       Radius of cylindrical roller(r) = 
40
2
 = 20 cm 
       Length of cylindrical roller (h) =140 cm 
Curved surface area of cylindrical roller = 2 ???? h 
                                                                                      =2 ×
2 2
7
× 20 × 140 
                                                                                 =17600 cm
2     
=17600/10000    =1.76 m
2
 
 
Area covered in one revolution is = curved surface area of cylinder 
                                                                 = 1.76 m
2
 
Total Area of Playground= No. of revolutions × curved surface area of cylinder 
                                                 = 350×1.76  
                                                 =616 m
2
 
Area of Playground= 616 m
2
. 
 
Tip: Since the shape of 
roller is like cylinder, we 
will use formula for 
cylinder. 
 
Note: Since we are 
converting cm
2
 to m
2 
we 
need to divide it by 
100×100 
Page 3


Surface and volume of cube, cuboid, and cylinder 
 
Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per 
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. 
Given: For Cuboidal Room, 
            Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m 
            To find  cost of painting four walls we first need to find the surface area of four walls . 
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h 
 
 
 
     Vertical surface area of cuboid=180 m
2
. 
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting                                                                  
       =180×13 
                                                             =2340  
Therefore Cost of Painting the four wall is 2340 Rs 
 
Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what 
will be the weight of the pillar. 
Given: For Pillar [cuboid] 
            Length =600cm= 
600
100
=6m 
         Breadth =55cm= 
55
100
=0.55m 
           Height=25cm= 
25
100
=0.25m 
 
=2(10+5)×6 
 =2(15)×6 
=180 
 
                            
                            
l 
h 
b 
Tip: Remember to convert 
dimensions from cm to m as 
weight per cube is given in m
3 
Solution 
Volume of Beam pillar[cuboid]= ?? × ?? × h 
                                                          =6×0.55×0.25 
                                                          =0.825 m
3
 
Weight of pillar=Volume of pillar×weight of volume per m
3
 
                               =0.825×200 
                                =165 Kg 
Weight of pillar=165 Kg        
 
Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a 
playground. Find the area of playground in m
2
.  
Solution: The Diameter cylindrical roller =40 cm 
       Radius of cylindrical roller(r) = 
40
2
 = 20 cm 
       Length of cylindrical roller (h) =140 cm 
Curved surface area of cylindrical roller = 2 ???? h 
                                                                                      =2 ×
2 2
7
× 20 × 140 
                                                                                 =17600 cm
2     
=17600/10000    =1.76 m
2
 
 
Area covered in one revolution is = curved surface area of cylinder 
                                                                 = 1.76 m
2
 
Total Area of Playground= No. of revolutions × curved surface area of cylinder 
                                                 = 350×1.76  
                                                 =616 m
2
 
Area of Playground= 616 m
2
. 
 
Tip: Since the shape of 
roller is like cylinder, we 
will use formula for 
cylinder. 
 
Note: Since we are 
converting cm
2
 to m
2 
we 
need to divide it by 
100×100 
Q.4) The curved surface area of cylinder is 154 cm
2
. The total surface area of the cylinder is 
thrice the curved surface area. Find the volume of cylinder.[ p=22/7] 
Given: curved surface area of cylinder (2 ???? h )= 154 cm
2 
Solution 
 
 
 
 
 
 
 
 
 
 
Curved surface area of cylinder ( ???? ?? ?? )= 154 cm
2
 
                                                                ?? ×
????
?? × ?? × ?? = ?????? 
                                                                         h= 
?????? 
?? × ????
                                                                                             
h= ?? . ??   cm 
Volume of Cylinder= ?? ?? ?? ?? 
                                 = 
????
?? × ?? × ?? × ?? . ?? 
                                   = 539 cm
3 
Volume of Cylinder= 539 cm
3   
 
 
 
: 
  
Total surface area of cylinder= 2 ×curved surface area
 
                               2 ???? h + 2 ?? ?? 2
= 3 × 154 
                                    154 +2 pr
2 
= 462 
                                      2 pr
2
=462– 154 
                                                2 pr
2
 =308 
                                     2 ×
2 2
7
× ?? 2
= 308 
                                                     r
2
= 
3 0 8 × 7
2× 2 2
      
                                                    r
2
=49 
r=7      
                                                       
Page 4


Surface and volume of cube, cuboid, and cylinder 
 
Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per 
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. 
Given: For Cuboidal Room, 
            Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m 
            To find  cost of painting four walls we first need to find the surface area of four walls . 
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h 
 
 
 
     Vertical surface area of cuboid=180 m
2
. 
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting                                                                  
       =180×13 
                                                             =2340  
Therefore Cost of Painting the four wall is 2340 Rs 
 
Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what 
will be the weight of the pillar. 
Given: For Pillar [cuboid] 
            Length =600cm= 
600
100
=6m 
         Breadth =55cm= 
55
100
=0.55m 
           Height=25cm= 
25
100
=0.25m 
 
=2(10+5)×6 
 =2(15)×6 
=180 
 
                            
                            
l 
h 
b 
Tip: Remember to convert 
dimensions from cm to m as 
weight per cube is given in m
3 
Solution 
Volume of Beam pillar[cuboid]= ?? × ?? × h 
                                                          =6×0.55×0.25 
                                                          =0.825 m
3
 
Weight of pillar=Volume of pillar×weight of volume per m
3
 
                               =0.825×200 
                                =165 Kg 
Weight of pillar=165 Kg        
 
Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a 
playground. Find the area of playground in m
2
.  
Solution: The Diameter cylindrical roller =40 cm 
       Radius of cylindrical roller(r) = 
40
2
 = 20 cm 
       Length of cylindrical roller (h) =140 cm 
Curved surface area of cylindrical roller = 2 ???? h 
                                                                                      =2 ×
2 2
7
× 20 × 140 
                                                                                 =17600 cm
2     
=17600/10000    =1.76 m
2
 
 
Area covered in one revolution is = curved surface area of cylinder 
                                                                 = 1.76 m
2
 
Total Area of Playground= No. of revolutions × curved surface area of cylinder 
                                                 = 350×1.76  
                                                 =616 m
2
 
Area of Playground= 616 m
2
. 
 
Tip: Since the shape of 
roller is like cylinder, we 
will use formula for 
cylinder. 
 
Note: Since we are 
converting cm
2
 to m
2 
we 
need to divide it by 
100×100 
Q.4) The curved surface area of cylinder is 154 cm
2
. The total surface area of the cylinder is 
thrice the curved surface area. Find the volume of cylinder.[ p=22/7] 
Given: curved surface area of cylinder (2 ???? h )= 154 cm
2 
Solution 
 
 
 
 
 
 
 
 
 
 
Curved surface area of cylinder ( ???? ?? ?? )= 154 cm
2
 
                                                                ?? ×
????
?? × ?? × ?? = ?????? 
                                                                         h= 
?????? 
?? × ????
                                                                                             
h= ?? . ??   cm 
Volume of Cylinder= ?? ?? ?? ?? 
                                 = 
????
?? × ?? × ?? × ?? . ?? 
                                   = 539 cm
3 
Volume of Cylinder= 539 cm
3   
 
 
 
: 
  
Total surface area of cylinder= 2 ×curved surface area
 
                               2 ???? h + 2 ?? ?? 2
= 3 × 154 
                                    154 +2 pr
2 
= 462 
                                      2 pr
2
=462– 154 
                                                2 pr
2
 =308 
                                     2 ×
2 2
7
× ?? 2
= 308 
                                                     r
2
= 
3 0 8 × 7
2× 2 2
      
                                                    r
2
=49 
r=7      
                                                       
Surface area and volume of Cone and Frustrum 
 
Q.1) The height of cone is 4 cm and radius is 3 cm. what will be its Total surface area 
and volume? 
Given: Radius of cone(r) = 3 cm 
            Height of cone(h) = 4 cm 
Solution: 
First we will find slant height of cone (l) = v h
2
+ ?? 2
 
                                                                   l = v4
2
+ 3
2
 
                                                                  l = v16 + 9 
                                             l = v25 
                                                                  l = 5 cm 
Total Surface Area of Cone = ???? ( ?? + ?? ) 
                                                 =  
2 2
7
 × 3 × (3 + 5) 
     =  
2 2
7
 × 3 × 8 
         = 75.428 cm
2 
Volume of cone = 
1
3
?? ?? 2
h 
      = 
1
3
×
2 2
7
× 3
2
× 4 
                        = 
22×3×4
7
 
                        =37.714 cm
3
 
 
 
Page 5


Surface and volume of cube, cuboid, and cylinder 
 
Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per 
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. 
Given: For Cuboidal Room, 
            Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m 
            To find  cost of painting four walls we first need to find the surface area of four walls . 
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h 
 
 
 
     Vertical surface area of cuboid=180 m
2
. 
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting                                                                  
       =180×13 
                                                             =2340  
Therefore Cost of Painting the four wall is 2340 Rs 
 
Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what 
will be the weight of the pillar. 
Given: For Pillar [cuboid] 
            Length =600cm= 
600
100
=6m 
         Breadth =55cm= 
55
100
=0.55m 
           Height=25cm= 
25
100
=0.25m 
 
=2(10+5)×6 
 =2(15)×6 
=180 
 
                            
                            
l 
h 
b 
Tip: Remember to convert 
dimensions from cm to m as 
weight per cube is given in m
3 
Solution 
Volume of Beam pillar[cuboid]= ?? × ?? × h 
                                                          =6×0.55×0.25 
                                                          =0.825 m
3
 
Weight of pillar=Volume of pillar×weight of volume per m
3
 
                               =0.825×200 
                                =165 Kg 
Weight of pillar=165 Kg        
 
Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a 
playground. Find the area of playground in m
2
.  
Solution: The Diameter cylindrical roller =40 cm 
       Radius of cylindrical roller(r) = 
40
2
 = 20 cm 
       Length of cylindrical roller (h) =140 cm 
Curved surface area of cylindrical roller = 2 ???? h 
                                                                                      =2 ×
2 2
7
× 20 × 140 
                                                                                 =17600 cm
2     
=17600/10000    =1.76 m
2
 
 
Area covered in one revolution is = curved surface area of cylinder 
                                                                 = 1.76 m
2
 
Total Area of Playground= No. of revolutions × curved surface area of cylinder 
                                                 = 350×1.76  
                                                 =616 m
2
 
Area of Playground= 616 m
2
. 
 
Tip: Since the shape of 
roller is like cylinder, we 
will use formula for 
cylinder. 
 
Note: Since we are 
converting cm
2
 to m
2 
we 
need to divide it by 
100×100 
Q.4) The curved surface area of cylinder is 154 cm
2
. The total surface area of the cylinder is 
thrice the curved surface area. Find the volume of cylinder.[ p=22/7] 
Given: curved surface area of cylinder (2 ???? h )= 154 cm
2 
Solution 
 
 
 
 
 
 
 
 
 
 
Curved surface area of cylinder ( ???? ?? ?? )= 154 cm
2
 
                                                                ?? ×
????
?? × ?? × ?? = ?????? 
                                                                         h= 
?????? 
?? × ????
                                                                                             
h= ?? . ??   cm 
Volume of Cylinder= ?? ?? ?? ?? 
                                 = 
????
?? × ?? × ?? × ?? . ?? 
                                   = 539 cm
3 
Volume of Cylinder= 539 cm
3   
 
 
 
: 
  
Total surface area of cylinder= 2 ×curved surface area
 
                               2 ???? h + 2 ?? ?? 2
= 3 × 154 
                                    154 +2 pr
2 
= 462 
                                      2 pr
2
=462– 154 
                                                2 pr
2
 =308 
                                     2 ×
2 2
7
× ?? 2
= 308 
                                                     r
2
= 
3 0 8 × 7
2× 2 2
      
                                                    r
2
=49 
r=7      
                                                       
Surface area and volume of Cone and Frustrum 
 
Q.1) The height of cone is 4 cm and radius is 3 cm. what will be its Total surface area 
and volume? 
Given: Radius of cone(r) = 3 cm 
            Height of cone(h) = 4 cm 
Solution: 
First we will find slant height of cone (l) = v h
2
+ ?? 2
 
                                                                   l = v4
2
+ 3
2
 
                                                                  l = v16 + 9 
                                             l = v25 
                                                                  l = 5 cm 
Total Surface Area of Cone = ???? ( ?? + ?? ) 
                                                 =  
2 2
7
 × 3 × (3 + 5) 
     =  
2 2
7
 × 3 × 8 
         = 75.428 cm
2 
Volume of cone = 
1
3
?? ?? 2
h 
      = 
1
3
×
2 2
7
× 3
2
× 4 
                        = 
22×3×4
7
 
                        =37.714 cm
3
 
 
 
Q.2) The volume of the cone is 352 cm
3 
and its height is 21 cm what will be the radius of 
cone? 
Given: volume of cone (v)= 352 cm
3
 
                Height of cone = 21 cm 
Solution       
 Volume of cone (v) = 
1
3
?? ?? 2
h 
                                  352= 
1
3
×
2 2
7
× ?? 2
× 21 
                                  
3 5 2
2 2
= ?? 2
 
                                   16 = ?? 2
    
                                  ? ?? = 4    ( ?? ?? ???? ???? ?????? ?? ???? ?????? h ???? ???? ) 
Ans: The radius of cone is 4 cm. 
 
Q.3)The height of frustum is 4 cm and it’s radii are 6 cm and 3 cm. Find  curved surface 
area and volume of frustum. 
Given: Height of frustum (h) = 4 cm 
            Base Radius (r
1
) = 6 cm 
            Upper Radius (r
2
) =3 cm 
Solution: 
Slant Height of the Frustum (l) = ? h
2
+ ( ?? 1
- ?? 2)
2
 
                                                  l = ?4
2
+ (6 - 3)
2
 
                                                  l = v16 + 9 
                                                  l = v25 
                                                  l =5 cm 
Curved surface area of frustum = ?? ( ?? 1
+ ?? 2
) ??         
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