Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.3
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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 21.3 PAGE NO: 21.22
1. Find the surface area of a cuboid whose
(i) length = 10 cm, breadth = 12 cm, height = 14 cm
(ii) length = 6 dm, breadth = 8 dm, height = 10 dm
(iii) length = 2m, breadth = 4 m, height = 5 m
(iv) length = 3.2 m, breadth = 30 dm, height = 250 cm.
Solution:
(i) Given details are,
Length of a cuboid = 10 cm
Breadth of a cuboid = 12 cm
Height of a cuboid = 14 cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (10×12 + 12×14 + 14×10)
= 2 (120 + 168 + 140)
= 2 (428)
= 856 cm
2
(ii) Given details are,
Length of a cuboid = 6 dm
Breadth of a cuboid = 8 dm
Height of a cuboid = 10 dm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (6×8 + 8×10 + 10×6)
= 2 (48 + 80 + 60)
= 2 (188)
= 376 dm
2
(iii) Given details are,
Length of a cuboid = 2m
Breadth of a cuboid = 4m
Height of a cuboid = 5m
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (2×4 + 4×5 + 5×2)
= 2 (8 + 20 + 10)
= 2 (38)
Page 2
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.3 PAGE NO: 21.22
1. Find the surface area of a cuboid whose
(i) length = 10 cm, breadth = 12 cm, height = 14 cm
(ii) length = 6 dm, breadth = 8 dm, height = 10 dm
(iii) length = 2m, breadth = 4 m, height = 5 m
(iv) length = 3.2 m, breadth = 30 dm, height = 250 cm.
Solution:
(i) Given details are,
Length of a cuboid = 10 cm
Breadth of a cuboid = 12 cm
Height of a cuboid = 14 cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (10×12 + 12×14 + 14×10)
= 2 (120 + 168 + 140)
= 2 (428)
= 856 cm
2
(ii) Given details are,
Length of a cuboid = 6 dm
Breadth of a cuboid = 8 dm
Height of a cuboid = 10 dm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (6×8 + 8×10 + 10×6)
= 2 (48 + 80 + 60)
= 2 (188)
= 376 dm
2
(iii) Given details are,
Length of a cuboid = 2m
Breadth of a cuboid = 4m
Height of a cuboid = 5m
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (2×4 + 4×5 + 5×2)
= 2 (8 + 20 + 10)
= 2 (38)
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
= 76 m
2
(iv) Given details are,
Length of a cuboid = 3.2 m= 32 dm
Breadth of a cuboid = 30 dm
Height of a cuboid = 250 cm= 25 dm
We know that,
surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (32×30 + 30×25 + 25×32)
= 2 (960 + 750 + 800)
= 2 (2510)
= 5020 dm
2
2. Find the surface area of a cube whose edge is
(i) 1.2 m
(ii) 27 cm
(iii) 3 cm
(iv) 6 m
(v) 2.1 m
Solution:
(i) Given,
Edge of cube = 1.2 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 1.2
2
= 6 × 1.44
= 8.64 m
2
(ii) Given,
Edge of cube = 27 cm
We know that,
Surface area of cube = 6 × side
2
= 6 × 27
2
= 6 × 729
= 4374 cm
2
(iii) Given,
Edge of cube = 3 cm
We know that,
Page 3
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.3 PAGE NO: 21.22
1. Find the surface area of a cuboid whose
(i) length = 10 cm, breadth = 12 cm, height = 14 cm
(ii) length = 6 dm, breadth = 8 dm, height = 10 dm
(iii) length = 2m, breadth = 4 m, height = 5 m
(iv) length = 3.2 m, breadth = 30 dm, height = 250 cm.
Solution:
(i) Given details are,
Length of a cuboid = 10 cm
Breadth of a cuboid = 12 cm
Height of a cuboid = 14 cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (10×12 + 12×14 + 14×10)
= 2 (120 + 168 + 140)
= 2 (428)
= 856 cm
2
(ii) Given details are,
Length of a cuboid = 6 dm
Breadth of a cuboid = 8 dm
Height of a cuboid = 10 dm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (6×8 + 8×10 + 10×6)
= 2 (48 + 80 + 60)
= 2 (188)
= 376 dm
2
(iii) Given details are,
Length of a cuboid = 2m
Breadth of a cuboid = 4m
Height of a cuboid = 5m
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (2×4 + 4×5 + 5×2)
= 2 (8 + 20 + 10)
= 2 (38)
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
= 76 m
2
(iv) Given details are,
Length of a cuboid = 3.2 m= 32 dm
Breadth of a cuboid = 30 dm
Height of a cuboid = 250 cm= 25 dm
We know that,
surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (32×30 + 30×25 + 25×32)
= 2 (960 + 750 + 800)
= 2 (2510)
= 5020 dm
2
2. Find the surface area of a cube whose edge is
(i) 1.2 m
(ii) 27 cm
(iii) 3 cm
(iv) 6 m
(v) 2.1 m
Solution:
(i) Given,
Edge of cube = 1.2 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 1.2
2
= 6 × 1.44
= 8.64 m
2
(ii) Given,
Edge of cube = 27 cm
We know that,
Surface area of cube = 6 × side
2
= 6 × 27
2
= 6 × 729
= 4374 cm
2
(iii) Given,
Edge of cube = 3 cm
We know that,
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Surface area of cube = 6 × side
2
= 6 × 3
2
= 6 × 9
= 54 cm
2
(iv) Given,
Edge of cube = 6 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 6
2
= 6 × 36
= 216 m
2
(v) Given,
Edge of cube = 2.1 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 2.1
2
= 6 × 4.41
= 26.46 m
2
3. A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
Solution:
Given details are,
Dimensions of cuboidal box = 5cm × 5cm × 4cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (5×5 + 5×4 + 4×5)
= 2 (25 + 20 + 20)
= 2 (65)
= 130 cm
2
4. Find the surface area of a cube whose volume is
(i) 343 m
3
(ii) 216 dm
3
Solution:
(i) Given details are,
Volume of cube = 343 m
3
Side of cube, a =
3
v(343) = 7m
Page 4
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.3 PAGE NO: 21.22
1. Find the surface area of a cuboid whose
(i) length = 10 cm, breadth = 12 cm, height = 14 cm
(ii) length = 6 dm, breadth = 8 dm, height = 10 dm
(iii) length = 2m, breadth = 4 m, height = 5 m
(iv) length = 3.2 m, breadth = 30 dm, height = 250 cm.
Solution:
(i) Given details are,
Length of a cuboid = 10 cm
Breadth of a cuboid = 12 cm
Height of a cuboid = 14 cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (10×12 + 12×14 + 14×10)
= 2 (120 + 168 + 140)
= 2 (428)
= 856 cm
2
(ii) Given details are,
Length of a cuboid = 6 dm
Breadth of a cuboid = 8 dm
Height of a cuboid = 10 dm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (6×8 + 8×10 + 10×6)
= 2 (48 + 80 + 60)
= 2 (188)
= 376 dm
2
(iii) Given details are,
Length of a cuboid = 2m
Breadth of a cuboid = 4m
Height of a cuboid = 5m
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (2×4 + 4×5 + 5×2)
= 2 (8 + 20 + 10)
= 2 (38)
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
= 76 m
2
(iv) Given details are,
Length of a cuboid = 3.2 m= 32 dm
Breadth of a cuboid = 30 dm
Height of a cuboid = 250 cm= 25 dm
We know that,
surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (32×30 + 30×25 + 25×32)
= 2 (960 + 750 + 800)
= 2 (2510)
= 5020 dm
2
2. Find the surface area of a cube whose edge is
(i) 1.2 m
(ii) 27 cm
(iii) 3 cm
(iv) 6 m
(v) 2.1 m
Solution:
(i) Given,
Edge of cube = 1.2 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 1.2
2
= 6 × 1.44
= 8.64 m
2
(ii) Given,
Edge of cube = 27 cm
We know that,
Surface area of cube = 6 × side
2
= 6 × 27
2
= 6 × 729
= 4374 cm
2
(iii) Given,
Edge of cube = 3 cm
We know that,
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Surface area of cube = 6 × side
2
= 6 × 3
2
= 6 × 9
= 54 cm
2
(iv) Given,
Edge of cube = 6 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 6
2
= 6 × 36
= 216 m
2
(v) Given,
Edge of cube = 2.1 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 2.1
2
= 6 × 4.41
= 26.46 m
2
3. A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
Solution:
Given details are,
Dimensions of cuboidal box = 5cm × 5cm × 4cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (5×5 + 5×4 + 4×5)
= 2 (25 + 20 + 20)
= 2 (65)
= 130 cm
2
4. Find the surface area of a cube whose volume is
(i) 343 m
3
(ii) 216 dm
3
Solution:
(i) Given details are,
Volume of cube = 343 m
3
Side of cube, a =
3
v(343) = 7m
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
We know that,
Surface area of cube = 6 × side
2
= 6 × 7
2
= 6 × 49
= 294 m
2
(ii) Given details are,
Volume of cube = 216 dm
3
Side of cube a =
3
v(216) = 6dm
We know that,
Surface area of cube = 6 × side
2
= 6 × 6
2
= 6 × 36
= 216 dm
2
5. Find the volume of a cube whose surface area is
(i) 96 cm
2
(ii) 150 m
2
Solution:
(i) Given details are,
Surface area of cube = 96 cm
2
6 × side
2
= 96cm
2
Side
2
= 96/6
= 16
Side = v16 = 4cm
? Volume of a cube = 4
3
= 64cm
3
(ii) Given details are,
Surface area of cube = 150 m
2
6 × side
2
= 150cm
2
Side
2
= 150/6
= 25
Side = v25 = 5cm
? Volume of a cube = 5
3
= 125m
3
6. The dimensions of a cuboid are in the ratio 5: 3: 1 and its total surface area is 414
m
2
. Find the dimensions.
Solution:
Given details are,
Page 5
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
EXERCISE 21.3 PAGE NO: 21.22
1. Find the surface area of a cuboid whose
(i) length = 10 cm, breadth = 12 cm, height = 14 cm
(ii) length = 6 dm, breadth = 8 dm, height = 10 dm
(iii) length = 2m, breadth = 4 m, height = 5 m
(iv) length = 3.2 m, breadth = 30 dm, height = 250 cm.
Solution:
(i) Given details are,
Length of a cuboid = 10 cm
Breadth of a cuboid = 12 cm
Height of a cuboid = 14 cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (10×12 + 12×14 + 14×10)
= 2 (120 + 168 + 140)
= 2 (428)
= 856 cm
2
(ii) Given details are,
Length of a cuboid = 6 dm
Breadth of a cuboid = 8 dm
Height of a cuboid = 10 dm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (6×8 + 8×10 + 10×6)
= 2 (48 + 80 + 60)
= 2 (188)
= 376 dm
2
(iii) Given details are,
Length of a cuboid = 2m
Breadth of a cuboid = 4m
Height of a cuboid = 5m
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (2×4 + 4×5 + 5×2)
= 2 (8 + 20 + 10)
= 2 (38)
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
= 76 m
2
(iv) Given details are,
Length of a cuboid = 3.2 m= 32 dm
Breadth of a cuboid = 30 dm
Height of a cuboid = 250 cm= 25 dm
We know that,
surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (32×30 + 30×25 + 25×32)
= 2 (960 + 750 + 800)
= 2 (2510)
= 5020 dm
2
2. Find the surface area of a cube whose edge is
(i) 1.2 m
(ii) 27 cm
(iii) 3 cm
(iv) 6 m
(v) 2.1 m
Solution:
(i) Given,
Edge of cube = 1.2 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 1.2
2
= 6 × 1.44
= 8.64 m
2
(ii) Given,
Edge of cube = 27 cm
We know that,
Surface area of cube = 6 × side
2
= 6 × 27
2
= 6 × 729
= 4374 cm
2
(iii) Given,
Edge of cube = 3 cm
We know that,
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Surface area of cube = 6 × side
2
= 6 × 3
2
= 6 × 9
= 54 cm
2
(iv) Given,
Edge of cube = 6 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 6
2
= 6 × 36
= 216 m
2
(v) Given,
Edge of cube = 2.1 m
We know that,
Surface area of cube = 6 × side
2
= 6 × 2.1
2
= 6 × 4.41
= 26.46 m
2
3. A cuboidal box is 5 cm by 5 cm by 4 cm. Find its surface area.
Solution:
Given details are,
Dimensions of cuboidal box = 5cm × 5cm × 4cm
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
= 2 (5×5 + 5×4 + 4×5)
= 2 (25 + 20 + 20)
= 2 (65)
= 130 cm
2
4. Find the surface area of a cube whose volume is
(i) 343 m
3
(ii) 216 dm
3
Solution:
(i) Given details are,
Volume of cube = 343 m
3
Side of cube, a =
3
v(343) = 7m
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
We know that,
Surface area of cube = 6 × side
2
= 6 × 7
2
= 6 × 49
= 294 m
2
(ii) Given details are,
Volume of cube = 216 dm
3
Side of cube a =
3
v(216) = 6dm
We know that,
Surface area of cube = 6 × side
2
= 6 × 6
2
= 6 × 36
= 216 dm
2
5. Find the volume of a cube whose surface area is
(i) 96 cm
2
(ii) 150 m
2
Solution:
(i) Given details are,
Surface area of cube = 96 cm
2
6 × side
2
= 96cm
2
Side
2
= 96/6
= 16
Side = v16 = 4cm
? Volume of a cube = 4
3
= 64cm
3
(ii) Given details are,
Surface area of cube = 150 m
2
6 × side
2
= 150cm
2
Side
2
= 150/6
= 25
Side = v25 = 5cm
? Volume of a cube = 5
3
= 125m
3
6. The dimensions of a cuboid are in the ratio 5: 3: 1 and its total surface area is 414
m
2
. Find the dimensions.
Solution:
Given details are,
RD Sharma Solutions for Class 8 Maths Chapter 21 – Mensuration –
II (Volumes and Surface Areas of a Cuboid and a Cube)
Ratio of dimensions of a cuboid = 5:3:1
Total surface area of cuboid = 414 m
2
The dimensions are = 5x × 3x × x
Surface area of cuboid = 414 m
2
We know that,
Surface area of cuboid = 2 (lb + bh + hl) cm
2
2 (lb + bh + hl) cm
2
= 414
2 (15x
2
+ 3x
2
+ 5x
2
) = 414
2 (23x
2
) = 414
46x
2
= 414
x
2
= 414/46
= 9
x = v9
= 3
? Dimensions are,
5x = 5 (3) = 15m
3x = 3 (3) = 9m
x = 3m
7. Find the area of the cardboard required to make a closed box of length 25 cm, 0.5
m and height 15 cm.
Solution:
Given details are,
Dimensions of closed box = 25cm × 0.5m × 15cm = 25cm × 50cm × 15cm
We know that,
Area of cardboard required = 2 (lb + bh + hl) cm
2
= 2 (25×50 + 50×15 + 15×25)
= 2 (1250 + 750 + 375)
= 2 (2375)
= 4750 cm
2
8. Find the surface area of a wooden box whose shape is of a cube, and if the edge of
the box is 12 cm.
Solution:
Given details are,
Edge of a cubic wooden box = 12 cm
We know that,
Surface area of cubic wooden box = 6 × side
2
= 6 × 12
2
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Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.3 on the App
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The content of Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.3 is prepared as per the latest Class 8 syllabus.
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