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
Students of Class 8 can study Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.3 alongwith tests & analysis from the EduRev app,
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students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
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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