Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.1
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Page 1
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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Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.1 Notes
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Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.1 Class 8 Questions
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