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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 21.3                                                 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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Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube) - EXERCISE 21.3 | Mathematics (Maths) Class 8

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