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RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
EXERCISE 21.1                                                  PAGE NO: 21.8 
 
1. Find the volume of a cuboid whose  
(i) length = 12 cm, breadth = 8 cm, height = 6 cm  
(ii) length = 1.2 m, breadth = 30 cm, height = 15 cm  
(iii) length = 15 cm, breadth = 2.5 dm, height = 8 cm. 
Solution: 
(i) The given details are: 
Length of a cuboid = 12 cm 
Breadth of a cuboid = 8 cm 
Height of a cuboid = 6 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 12 × 8 ×6  
                                 = 576 cm
3
 
 
(ii) The given details are: 
Length of a cuboid = 1.2 m = 120 cm 
Breadth of a cuboid = 30 cm 
Height of a cuboid = 15 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 120 × 30 × 15  
                                 = 54000 cm
3
 
 
(iii) The given details are: 
Length of a cuboid = 15 cm 
Breadth of a cuboid = 2.5 dm = 25 cm 
Height of a cuboid = 8 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 15 × 25 × 8  
                                 = 3000 cm
3
 
 
2. Find the volume of a cube whose side is  
(i) 4 cm (ii) 8 cm  
(iii) 1.5 dm (iv) 1.2 m  
(v) 25 mm 
Solution: 
Page 2


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
EXERCISE 21.1                                                  PAGE NO: 21.8 
 
1. Find the volume of a cuboid whose  
(i) length = 12 cm, breadth = 8 cm, height = 6 cm  
(ii) length = 1.2 m, breadth = 30 cm, height = 15 cm  
(iii) length = 15 cm, breadth = 2.5 dm, height = 8 cm. 
Solution: 
(i) The given details are: 
Length of a cuboid = 12 cm 
Breadth of a cuboid = 8 cm 
Height of a cuboid = 6 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 12 × 8 ×6  
                                 = 576 cm
3
 
 
(ii) The given details are: 
Length of a cuboid = 1.2 m = 120 cm 
Breadth of a cuboid = 30 cm 
Height of a cuboid = 15 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 120 × 30 × 15  
                                 = 54000 cm
3
 
 
(iii) The given details are: 
Length of a cuboid = 15 cm 
Breadth of a cuboid = 2.5 dm = 25 cm 
Height of a cuboid = 8 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 15 × 25 × 8  
                                 = 3000 cm
3
 
 
2. Find the volume of a cube whose side is  
(i) 4 cm (ii) 8 cm  
(iii) 1.5 dm (iv) 1.2 m  
(v) 25 mm 
Solution: 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
(i) Given details are, 
Side of cube = 4 cm 
Volume of cube = (side)
 3
  
                           = 4
3
 = 64 cm
3
 
 
(ii) Given details are, 
Side of cube = 8 cm 
Volume of cube = (side)
 3
  
                           = 8
3
 = 512 cm
3
 
 
(iii) Given details are, 
Side of cube = 1.5 dm 
Volume of cube = (side)
 3
  
                          = 1.5
3
 = 3.375 dm
3
 = 3375 cm
3
 
 
(iv) Given details are, 
Side of cube = 1.2 m 
Volume of cube = (side)
 3
  
                           = 1.2
3
 = 1.728 m
3
 
 
(v) Given details are, 
Side of cube = 25 mm 
Volume of cube = (side)
 3
  
                           = 25
3
 = 15625 mm
3
= 15.625 cm
3
 
 
3. Find the height of a cuboid of volume 100 cm
3
, whose length and breadth are 5 cm 
and 4 cm respectively. 
Solution: 
Given details are, 
Volume of a cuboid = 100 cm
3
 
Length of a cuboid = 5 cm 
Breadth of a cuboid = 4 cm 
Let height of cuboid be ‘h’ cm 
We know that, l × b × h = 100cm 
h = 100/( l × b) 
   = 100/(5×4) 
   = 5cm 
 
4. A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 
Page 3


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
EXERCISE 21.1                                                  PAGE NO: 21.8 
 
1. Find the volume of a cuboid whose  
(i) length = 12 cm, breadth = 8 cm, height = 6 cm  
(ii) length = 1.2 m, breadth = 30 cm, height = 15 cm  
(iii) length = 15 cm, breadth = 2.5 dm, height = 8 cm. 
Solution: 
(i) The given details are: 
Length of a cuboid = 12 cm 
Breadth of a cuboid = 8 cm 
Height of a cuboid = 6 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 12 × 8 ×6  
                                 = 576 cm
3
 
 
(ii) The given details are: 
Length of a cuboid = 1.2 m = 120 cm 
Breadth of a cuboid = 30 cm 
Height of a cuboid = 15 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 120 × 30 × 15  
                                 = 54000 cm
3
 
 
(iii) The given details are: 
Length of a cuboid = 15 cm 
Breadth of a cuboid = 2.5 dm = 25 cm 
Height of a cuboid = 8 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 15 × 25 × 8  
                                 = 3000 cm
3
 
 
2. Find the volume of a cube whose side is  
(i) 4 cm (ii) 8 cm  
(iii) 1.5 dm (iv) 1.2 m  
(v) 25 mm 
Solution: 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
(i) Given details are, 
Side of cube = 4 cm 
Volume of cube = (side)
 3
  
                           = 4
3
 = 64 cm
3
 
 
(ii) Given details are, 
Side of cube = 8 cm 
Volume of cube = (side)
 3
  
                           = 8
3
 = 512 cm
3
 
 
(iii) Given details are, 
Side of cube = 1.5 dm 
Volume of cube = (side)
 3
  
                          = 1.5
3
 = 3.375 dm
3
 = 3375 cm
3
 
 
(iv) Given details are, 
Side of cube = 1.2 m 
Volume of cube = (side)
 3
  
                           = 1.2
3
 = 1.728 m
3
 
 
(v) Given details are, 
Side of cube = 25 mm 
Volume of cube = (side)
 3
  
                           = 25
3
 = 15625 mm
3
= 15.625 cm
3
 
 
3. Find the height of a cuboid of volume 100 cm
3
, whose length and breadth are 5 cm 
and 4 cm respectively. 
Solution: 
Given details are, 
Volume of a cuboid = 100 cm
3
 
Length of a cuboid = 5 cm 
Breadth of a cuboid = 4 cm 
Let height of cuboid be ‘h’ cm 
We know that, l × b × h = 100cm 
h = 100/( l × b) 
   = 100/(5×4) 
   = 5cm 
 
4. A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
300 cm
3
 of a liquid? 
Solution: 
Given details are, 
Volume of a liquid in the vessel = 300 cm
3
 
Length of a cuboidal vessel = 10 cm 
Breadth of a cuboidal vessel = 5 cm 
Let height of cuboidal vessel be ‘h’ cm 
We know that, l × b × h = 300 cm
3
 
h = 300/(l × b) 
   = 300/(10×5) 
   = 6cm 
 
5. A milk container is 8 cm long and 50 cm wide. What should be its height so that it 
can hold 4 litres of milk? 
Solution: 
Given details are, 
Volume = 4 litres = 4000 cm
3
 
Length of a milk container = 8 cm 
Breadth of a milk container = 50 cm 
Let height of milk container be ‘h’ cm 
We know that, l × b × h = 4000 cm
3
 
h = 4000/ (l × b) 
   = 4000/ (50×8) 
   = 10cm 
 
6. A cuboidal wooden block contains 36 cm
3
 wood. If it be 4 cm long and 3 cm wide, 
find its height. 
Solution: 
Given details are, 
Volume of wooden block = 36 cm
3
 
Length of the wooden block = 4 cm 
Breadth of a wooden block = 3 cm 
Let height of wooden block be ‘h’ cm 
We know that, l × b × h = 36 cm
3
 
h = 36/( l × b) 
   = 36/(4×3) 
   = 3cm 
 
7. What will happen to the volume of a cube, if its edge is  
Page 4


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
EXERCISE 21.1                                                  PAGE NO: 21.8 
 
1. Find the volume of a cuboid whose  
(i) length = 12 cm, breadth = 8 cm, height = 6 cm  
(ii) length = 1.2 m, breadth = 30 cm, height = 15 cm  
(iii) length = 15 cm, breadth = 2.5 dm, height = 8 cm. 
Solution: 
(i) The given details are: 
Length of a cuboid = 12 cm 
Breadth of a cuboid = 8 cm 
Height of a cuboid = 6 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 12 × 8 ×6  
                                 = 576 cm
3
 
 
(ii) The given details are: 
Length of a cuboid = 1.2 m = 120 cm 
Breadth of a cuboid = 30 cm 
Height of a cuboid = 15 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 120 × 30 × 15  
                                 = 54000 cm
3
 
 
(iii) The given details are: 
Length of a cuboid = 15 cm 
Breadth of a cuboid = 2.5 dm = 25 cm 
Height of a cuboid = 8 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 15 × 25 × 8  
                                 = 3000 cm
3
 
 
2. Find the volume of a cube whose side is  
(i) 4 cm (ii) 8 cm  
(iii) 1.5 dm (iv) 1.2 m  
(v) 25 mm 
Solution: 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
(i) Given details are, 
Side of cube = 4 cm 
Volume of cube = (side)
 3
  
                           = 4
3
 = 64 cm
3
 
 
(ii) Given details are, 
Side of cube = 8 cm 
Volume of cube = (side)
 3
  
                           = 8
3
 = 512 cm
3
 
 
(iii) Given details are, 
Side of cube = 1.5 dm 
Volume of cube = (side)
 3
  
                          = 1.5
3
 = 3.375 dm
3
 = 3375 cm
3
 
 
(iv) Given details are, 
Side of cube = 1.2 m 
Volume of cube = (side)
 3
  
                           = 1.2
3
 = 1.728 m
3
 
 
(v) Given details are, 
Side of cube = 25 mm 
Volume of cube = (side)
 3
  
                           = 25
3
 = 15625 mm
3
= 15.625 cm
3
 
 
3. Find the height of a cuboid of volume 100 cm
3
, whose length and breadth are 5 cm 
and 4 cm respectively. 
Solution: 
Given details are, 
Volume of a cuboid = 100 cm
3
 
Length of a cuboid = 5 cm 
Breadth of a cuboid = 4 cm 
Let height of cuboid be ‘h’ cm 
We know that, l × b × h = 100cm 
h = 100/( l × b) 
   = 100/(5×4) 
   = 5cm 
 
4. A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
300 cm
3
 of a liquid? 
Solution: 
Given details are, 
Volume of a liquid in the vessel = 300 cm
3
 
Length of a cuboidal vessel = 10 cm 
Breadth of a cuboidal vessel = 5 cm 
Let height of cuboidal vessel be ‘h’ cm 
We know that, l × b × h = 300 cm
3
 
h = 300/(l × b) 
   = 300/(10×5) 
   = 6cm 
 
5. A milk container is 8 cm long and 50 cm wide. What should be its height so that it 
can hold 4 litres of milk? 
Solution: 
Given details are, 
Volume = 4 litres = 4000 cm
3
 
Length of a milk container = 8 cm 
Breadth of a milk container = 50 cm 
Let height of milk container be ‘h’ cm 
We know that, l × b × h = 4000 cm
3
 
h = 4000/ (l × b) 
   = 4000/ (50×8) 
   = 10cm 
 
6. A cuboidal wooden block contains 36 cm
3
 wood. If it be 4 cm long and 3 cm wide, 
find its height. 
Solution: 
Given details are, 
Volume of wooden block = 36 cm
3
 
Length of the wooden block = 4 cm 
Breadth of a wooden block = 3 cm 
Let height of wooden block be ‘h’ cm 
We know that, l × b × h = 36 cm
3
 
h = 36/( l × b) 
   = 36/(4×3) 
   = 3cm 
 
7. What will happen to the volume of a cube, if its edge is  
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
 
(i) halved (ii) trebled? 
Solution: 
Let us consider edge of a cube be ‘a’ cm 
Volume of a cube will be ‘a
3
’cm 
(i) When halved 
Edge = a/2 
Volume = (a/2)
3
 = a
3
/2
3
 = a
3
/8 = 1/8times 
 
(ii) When trebled 
Edge = 3a 
Volume = (3a)
3
 = 27a
3
 = 27times 
 
8. What will happen to the volume of a cuboid if its:  
(i) Length is doubled, height is same and breadth is halved? 
(ii) Length is doubled, height is doubled and breadth is same? 
Solution: 
Let us consider, 
Length of a cuboid be ‘l’ 
Breadth of a cuboid be ‘b’ 
Height of a cuboid be ‘h’ 
So, Volume of a cuboid = l × b × h 
Now, 
(i) Length of a cuboid becomes = 2l 
Breadth = b/2  
Height = h 
Volume of cuboid = 2l × b/2 × h = l × b × h (remains same)   
 
(ii) Length of a cuboid becomes = 2l 
Breadth = b 
Height = 2h 
Volume of cuboid = 2l × b × 2h = 4lbh (four times) 
 
9. Three cuboids of dimensions 5 cm × 6cm × 7cm, 4cm × 7cm × 8cm and 2 cm × 3 
cm × 13 cm are melted and a cube is made. Find the side of cube. 
Solution: 
Given details are, 
Volume of First cuboid = 5 × 6 × 7 = 210 cm
3
 
Volume of second cuboid = 4 × 7 × 8 = 224 cm
3
 
Page 5


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
EXERCISE 21.1                                                  PAGE NO: 21.8 
 
1. Find the volume of a cuboid whose  
(i) length = 12 cm, breadth = 8 cm, height = 6 cm  
(ii) length = 1.2 m, breadth = 30 cm, height = 15 cm  
(iii) length = 15 cm, breadth = 2.5 dm, height = 8 cm. 
Solution: 
(i) The given details are: 
Length of a cuboid = 12 cm 
Breadth of a cuboid = 8 cm 
Height of a cuboid = 6 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 12 × 8 ×6  
                                 = 576 cm
3
 
 
(ii) The given details are: 
Length of a cuboid = 1.2 m = 120 cm 
Breadth of a cuboid = 30 cm 
Height of a cuboid = 15 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 120 × 30 × 15  
                                 = 54000 cm
3
 
 
(iii) The given details are: 
Length of a cuboid = 15 cm 
Breadth of a cuboid = 2.5 dm = 25 cm 
Height of a cuboid = 8 cm 
By using the formula 
Volume of a cuboid = length × breadth × height  
                                 = 15 × 25 × 8  
                                 = 3000 cm
3
 
 
2. Find the volume of a cube whose side is  
(i) 4 cm (ii) 8 cm  
(iii) 1.5 dm (iv) 1.2 m  
(v) 25 mm 
Solution: 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
(i) Given details are, 
Side of cube = 4 cm 
Volume of cube = (side)
 3
  
                           = 4
3
 = 64 cm
3
 
 
(ii) Given details are, 
Side of cube = 8 cm 
Volume of cube = (side)
 3
  
                           = 8
3
 = 512 cm
3
 
 
(iii) Given details are, 
Side of cube = 1.5 dm 
Volume of cube = (side)
 3
  
                          = 1.5
3
 = 3.375 dm
3
 = 3375 cm
3
 
 
(iv) Given details are, 
Side of cube = 1.2 m 
Volume of cube = (side)
 3
  
                           = 1.2
3
 = 1.728 m
3
 
 
(v) Given details are, 
Side of cube = 25 mm 
Volume of cube = (side)
 3
  
                           = 25
3
 = 15625 mm
3
= 15.625 cm
3
 
 
3. Find the height of a cuboid of volume 100 cm
3
, whose length and breadth are 5 cm 
and 4 cm respectively. 
Solution: 
Given details are, 
Volume of a cuboid = 100 cm
3
 
Length of a cuboid = 5 cm 
Breadth of a cuboid = 4 cm 
Let height of cuboid be ‘h’ cm 
We know that, l × b × h = 100cm 
h = 100/( l × b) 
   = 100/(5×4) 
   = 5cm 
 
4. A cuboidal vessel is 10 cm long and 5 cm wide. How high it must be made to hold 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
300 cm
3
 of a liquid? 
Solution: 
Given details are, 
Volume of a liquid in the vessel = 300 cm
3
 
Length of a cuboidal vessel = 10 cm 
Breadth of a cuboidal vessel = 5 cm 
Let height of cuboidal vessel be ‘h’ cm 
We know that, l × b × h = 300 cm
3
 
h = 300/(l × b) 
   = 300/(10×5) 
   = 6cm 
 
5. A milk container is 8 cm long and 50 cm wide. What should be its height so that it 
can hold 4 litres of milk? 
Solution: 
Given details are, 
Volume = 4 litres = 4000 cm
3
 
Length of a milk container = 8 cm 
Breadth of a milk container = 50 cm 
Let height of milk container be ‘h’ cm 
We know that, l × b × h = 4000 cm
3
 
h = 4000/ (l × b) 
   = 4000/ (50×8) 
   = 10cm 
 
6. A cuboidal wooden block contains 36 cm
3
 wood. If it be 4 cm long and 3 cm wide, 
find its height. 
Solution: 
Given details are, 
Volume of wooden block = 36 cm
3
 
Length of the wooden block = 4 cm 
Breadth of a wooden block = 3 cm 
Let height of wooden block be ‘h’ cm 
We know that, l × b × h = 36 cm
3
 
h = 36/( l × b) 
   = 36/(4×3) 
   = 3cm 
 
7. What will happen to the volume of a cube, if its edge is  
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
 
(i) halved (ii) trebled? 
Solution: 
Let us consider edge of a cube be ‘a’ cm 
Volume of a cube will be ‘a
3
’cm 
(i) When halved 
Edge = a/2 
Volume = (a/2)
3
 = a
3
/2
3
 = a
3
/8 = 1/8times 
 
(ii) When trebled 
Edge = 3a 
Volume = (3a)
3
 = 27a
3
 = 27times 
 
8. What will happen to the volume of a cuboid if its:  
(i) Length is doubled, height is same and breadth is halved? 
(ii) Length is doubled, height is doubled and breadth is same? 
Solution: 
Let us consider, 
Length of a cuboid be ‘l’ 
Breadth of a cuboid be ‘b’ 
Height of a cuboid be ‘h’ 
So, Volume of a cuboid = l × b × h 
Now, 
(i) Length of a cuboid becomes = 2l 
Breadth = b/2  
Height = h 
Volume of cuboid = 2l × b/2 × h = l × b × h (remains same)   
 
(ii) Length of a cuboid becomes = 2l 
Breadth = b 
Height = 2h 
Volume of cuboid = 2l × b × 2h = 4lbh (four times) 
 
9. Three cuboids of dimensions 5 cm × 6cm × 7cm, 4cm × 7cm × 8cm and 2 cm × 3 
cm × 13 cm are melted and a cube is made. Find the side of cube. 
Solution: 
Given details are, 
Volume of First cuboid = 5 × 6 × 7 = 210 cm
3
 
Volume of second cuboid = 4 × 7 × 8 = 224 cm
3
 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration – 
II (Volumes and Surface Areas of a Cuboid and a Cube) 
 
Volume of third cuboid = 2 × 3 × 13 = 78 cm
3
 
So, Volume of a cube = 210 + 224 + 78 = 512 cm
3
 
Let side of a cube be ‘a’ 
a
3
 = 512 
? a = 8 cm 
 
10. Find the weight of solid rectangular iron piece of size 50 cm×40cm × 10 cm, if 1 
cm
3
 of iron weights 8 gm. 
Solution: 
Given details are, 
Dimension of rectangular iron piece = 50cm × 40cm × 10cm 
Volume of solid rectangular = 50 × 40 × 10 = 20000 cm
3
 
Weight of 1 cm
3
 iron = 8 gm. 
? Weight of 20000 cm
3
 iron = 8 × 20000  
                                              = 160000 gm. 
                                              = 160 kg 
 
11. How many wooden cubical blocks of side 25 cm can be cut from a log of wood of 
size 3 m by 75 cm by 50 cm, assuming that there is no wastage? 
Solution: 
Given details are, 
Dimensions of log of wood = 3m × 75cm × 50cm 
Side of cubical block = 25cm 
We know that, 
Number of cubical block that can be made from wooden log = 
Volume of wooden block / volume of cubical block  
= (300 × 75 × 50) / (25 × 25 × 25) 
= 72 blocks 
 
12. A cuboidal block of silver is 9 cm long, 4 cm broad and 3.5 cm in height. From it, 
beads of volume 1.5 cm
3
 each are to be made. Find the number of beads that can be 
made from the block. 
Solution: 
Given details are, 
Length of a cuboidal block of silver = 9cm 
Breadth = 4cm 
Height = 3.5cm 
Volume of a cuboid = l × b × h 
                                 = 9 × 4 × 3.5 = 126cm
3
 
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