Selina Textbook Solutions: Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) | Mathematics Class 8 ICSE PDF Download

 Page 1


21. Surface Area, Volume and Capacity  
(Cuboid, Cube and Cylinder) 
EXERCISE 21 (A) 
Question 1. 
Find the volume and the total surface area of a cuboid, whose : 
(i) length = 15 cm, breadth = 10 cm and height = 8 cm. 
(ii) l = 3.5 m, b = 2.6 m and h = 90 cm, 
Solution: 
(i) Length =15 cm, Breadth = 10 cm, Height = 8 cm. 
Volume of a cuboid = Length x Breadth x Height = 15 x 10 x 8 =1200 cm
3
. 
Total surface area of a cuboid 2 (l x b + b x h + h x l) = 2 (15 x 10 + 10 x 8 + 8 x 15) = 
2(150 + 80 +120) = 2 x 350 = 700 cm
2
 
(ii) Length = 3.5 m Breadth = 2.6 m, Height = 90 cm =  m = 0.9 m. 
Volume of a cuboid = l x b x h = 3.5 x 2.6 x 0.9 = 8.19 m
3
 
Total surface area of a cuboid = 2(l x b + b x h + h x l) 
= 2 (3.5 x 2.6 + 2.6 x 0.9 + 0.9 x 3.5) = 2 (910 + 2.34 + 3.15) = 2(14.59)= 29.18 m
2
 
Question 2. 
(i) The volume of a cuboid is 3456 cm
3
. If its length = 24 cm and breadth = 18 cm ; find 
its height. 
(ii) The volume of a cuboid is 7.68 m
3
. If its length = 3.2 m and height = 1.0 m; find its 
breadth. 
(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If 
the volume of the cuboid is 1.92 m
3
; find its length. 
Solution: 
(i) Volume of the given cuboid = 3456 cm
3
. 
Length of the given cuboid = 24 cm. 
Breadth of the given cuboid = 18 cm 
We know, 
Length x Breadth x Height = Volume of a cuboid 
? 24 x 18 x Height = 3456 
? Height =  
? Height =  
? Height = 8 cm 
(ii) Volume of a cuboid = 7.68 m
3
 
Length of a cuboid = 3.2 m 
Height of a cuboid = 10m 
We know 
Length x Breadth x Height = Volume of a cuboid 
3.2 x Breadth x 1.0 = 7.68 
? Breadth =  
Page 2


21. Surface Area, Volume and Capacity  
(Cuboid, Cube and Cylinder) 
EXERCISE 21 (A) 
Question 1. 
Find the volume and the total surface area of a cuboid, whose : 
(i) length = 15 cm, breadth = 10 cm and height = 8 cm. 
(ii) l = 3.5 m, b = 2.6 m and h = 90 cm, 
Solution: 
(i) Length =15 cm, Breadth = 10 cm, Height = 8 cm. 
Volume of a cuboid = Length x Breadth x Height = 15 x 10 x 8 =1200 cm
3
. 
Total surface area of a cuboid 2 (l x b + b x h + h x l) = 2 (15 x 10 + 10 x 8 + 8 x 15) = 
2(150 + 80 +120) = 2 x 350 = 700 cm
2
 
(ii) Length = 3.5 m Breadth = 2.6 m, Height = 90 cm =  m = 0.9 m. 
Volume of a cuboid = l x b x h = 3.5 x 2.6 x 0.9 = 8.19 m
3
 
Total surface area of a cuboid = 2(l x b + b x h + h x l) 
= 2 (3.5 x 2.6 + 2.6 x 0.9 + 0.9 x 3.5) = 2 (910 + 2.34 + 3.15) = 2(14.59)= 29.18 m
2
 
Question 2. 
(i) The volume of a cuboid is 3456 cm
3
. If its length = 24 cm and breadth = 18 cm ; find 
its height. 
(ii) The volume of a cuboid is 7.68 m
3
. If its length = 3.2 m and height = 1.0 m; find its 
breadth. 
(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If 
the volume of the cuboid is 1.92 m
3
; find its length. 
Solution: 
(i) Volume of the given cuboid = 3456 cm
3
. 
Length of the given cuboid = 24 cm. 
Breadth of the given cuboid = 18 cm 
We know, 
Length x Breadth x Height = Volume of a cuboid 
? 24 x 18 x Height = 3456 
? Height =  
? Height =  
? Height = 8 cm 
(ii) Volume of a cuboid = 7.68 m
3
 
Length of a cuboid = 3.2 m 
Height of a cuboid = 10m 
We know 
Length x Breadth x Height = Volume of a cuboid 
3.2 x Breadth x 1.0 = 7.68 
? Breadth =  
? Breadth =  
? Breadth = 2.4 m 
(iii) Volume of a rectangular solid = 1.92 m
3
 
Breadth of a rectangular solid = 1.20 m 
Height of a rectangular solid = 80 cm = 0.8 m 
We know 
Length x Breadth x Height = Volume of a rectangular solid (cubical) 
Length x 1.20 x 0.8 = 1.92 
Length x 0.96 = 1.92 
? Length =  
? Length =  
? Length = 2 m 
Question 3. 
The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 
cm
3
; find its dimensions. (Dimensions means : its length, breadth and height). Also find 
the total surface area of the cuboid. 
Solution: 
Let length of the given cuboid = 5x 
Breadth of the given cuboid = 3x 
Height of the given cuboid = 2x 
Volume of the given cuboid = Length x Breadth x Height 
= 5x x 3x x 2x = 30x
3
 
But we are given volume = 240 cm
3
 
30x
3
 = 240 cm
3
 
? x
3
 =  
? x
3
 = 8 
? x =  
? x =  
? x = 2 cm 
Length of the given cube = 5x = 5 x 2 = 10 cm 
Breadth of the given cube = 3x = 3 x 2 = 6 cm 
Height of the given cube = 2x = 2 x 2 = 4cm 
Total surface area of the given cuboid = 2(l x b + b x h + h x l) 
= 2(10 x 6 + 6 x 4 + 4 x 10) = 2(60 + 24 + 40) = 2 x 124 = 248 cm
2
 
Question 4. 
The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface 
area is 504 cm2; find its dimensions. Also, find the volume of the cuboid. 
Solution: 
Let length of the cuboid = 6x 
Breadth of the cuboid = 5x 
Height of the cuboid = 3x 
Total surface area of the given cuboid = 2 (I x b + b x h + h x l) 
Page 3


21. Surface Area, Volume and Capacity  
(Cuboid, Cube and Cylinder) 
EXERCISE 21 (A) 
Question 1. 
Find the volume and the total surface area of a cuboid, whose : 
(i) length = 15 cm, breadth = 10 cm and height = 8 cm. 
(ii) l = 3.5 m, b = 2.6 m and h = 90 cm, 
Solution: 
(i) Length =15 cm, Breadth = 10 cm, Height = 8 cm. 
Volume of a cuboid = Length x Breadth x Height = 15 x 10 x 8 =1200 cm
3
. 
Total surface area of a cuboid 2 (l x b + b x h + h x l) = 2 (15 x 10 + 10 x 8 + 8 x 15) = 
2(150 + 80 +120) = 2 x 350 = 700 cm
2
 
(ii) Length = 3.5 m Breadth = 2.6 m, Height = 90 cm =  m = 0.9 m. 
Volume of a cuboid = l x b x h = 3.5 x 2.6 x 0.9 = 8.19 m
3
 
Total surface area of a cuboid = 2(l x b + b x h + h x l) 
= 2 (3.5 x 2.6 + 2.6 x 0.9 + 0.9 x 3.5) = 2 (910 + 2.34 + 3.15) = 2(14.59)= 29.18 m
2
 
Question 2. 
(i) The volume of a cuboid is 3456 cm
3
. If its length = 24 cm and breadth = 18 cm ; find 
its height. 
(ii) The volume of a cuboid is 7.68 m
3
. If its length = 3.2 m and height = 1.0 m; find its 
breadth. 
(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If 
the volume of the cuboid is 1.92 m
3
; find its length. 
Solution: 
(i) Volume of the given cuboid = 3456 cm
3
. 
Length of the given cuboid = 24 cm. 
Breadth of the given cuboid = 18 cm 
We know, 
Length x Breadth x Height = Volume of a cuboid 
? 24 x 18 x Height = 3456 
? Height =  
? Height =  
? Height = 8 cm 
(ii) Volume of a cuboid = 7.68 m
3
 
Length of a cuboid = 3.2 m 
Height of a cuboid = 10m 
We know 
Length x Breadth x Height = Volume of a cuboid 
3.2 x Breadth x 1.0 = 7.68 
? Breadth =  
? Breadth =  
? Breadth = 2.4 m 
(iii) Volume of a rectangular solid = 1.92 m
3
 
Breadth of a rectangular solid = 1.20 m 
Height of a rectangular solid = 80 cm = 0.8 m 
We know 
Length x Breadth x Height = Volume of a rectangular solid (cubical) 
Length x 1.20 x 0.8 = 1.92 
Length x 0.96 = 1.92 
? Length =  
? Length =  
? Length = 2 m 
Question 3. 
The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 
cm
3
; find its dimensions. (Dimensions means : its length, breadth and height). Also find 
the total surface area of the cuboid. 
Solution: 
Let length of the given cuboid = 5x 
Breadth of the given cuboid = 3x 
Height of the given cuboid = 2x 
Volume of the given cuboid = Length x Breadth x Height 
= 5x x 3x x 2x = 30x
3
 
But we are given volume = 240 cm
3
 
30x
3
 = 240 cm
3
 
? x
3
 =  
? x
3
 = 8 
? x =  
? x =  
? x = 2 cm 
Length of the given cube = 5x = 5 x 2 = 10 cm 
Breadth of the given cube = 3x = 3 x 2 = 6 cm 
Height of the given cube = 2x = 2 x 2 = 4cm 
Total surface area of the given cuboid = 2(l x b + b x h + h x l) 
= 2(10 x 6 + 6 x 4 + 4 x 10) = 2(60 + 24 + 40) = 2 x 124 = 248 cm
2
 
Question 4. 
The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface 
area is 504 cm2; find its dimensions. Also, find the volume of the cuboid. 
Solution: 
Let length of the cuboid = 6x 
Breadth of the cuboid = 5x 
Height of the cuboid = 3x 
Total surface area of the given cuboid = 2 (I x b + b x h + h x l) 
= 2(6x x 5x + 5x x 3x + 3x x 6x) = 2(30×2 + 15×2 + 18×2) 
= 2 x 63×2 = 126x
2
 
But we are given total surface area of the given cuboid = 504 cm
2
 
126x
2
 = 504 cm
2
 
=> x
2
 =  
=> x
2
 = 4 
=> x = v4 
=> x = 2 cm. 
Length of the cuboid = 6x = 6 x 2 = 12 cm 
Breadth of the cuboid = 5x = 5 x 2 = 10cm 
Height of the cuboid = 3x = 3 x 2 = 6 cm 
Volume of the cuboid = l x b x h = 12 x 10 x 6 = 720 cm
3
 
Question 5. 
Find the volume and total surface area of a cube whose each edge is : 
(i) 8 cm 
(ii) 2 m 40 cm. 
Solution: 
(i) Edge of the given cube = 8 cm 
Volume of the given cube = (Edge)
3
 = (8)
3
 = 8 x 8 x 8 = 512 cm
3
 
Total surface area of a cube = 6(Edge)
2
 = 6 x (8)
2
 = 384 cm
2
 
(ii) Edge of the given cube = 2 m 40 cm = 2.40 m 
Volume of a cube = (Edge)
3
 
Volume of the given cube = (2.40)
3
 = 2.40 x 2.40 x 2.40 = 13.824 m
2
 
Total surface area of the given cube = 6 x 2.4 x 2.4 = 34.56 m
2
 
Question 6. 
Find the length of each edge of a cube, if its volume is : 
(i) 216 cm
3
 
(ii) 1.728 m
3
 
Page 4


21. Surface Area, Volume and Capacity  
(Cuboid, Cube and Cylinder) 
EXERCISE 21 (A) 
Question 1. 
Find the volume and the total surface area of a cuboid, whose : 
(i) length = 15 cm, breadth = 10 cm and height = 8 cm. 
(ii) l = 3.5 m, b = 2.6 m and h = 90 cm, 
Solution: 
(i) Length =15 cm, Breadth = 10 cm, Height = 8 cm. 
Volume of a cuboid = Length x Breadth x Height = 15 x 10 x 8 =1200 cm
3
. 
Total surface area of a cuboid 2 (l x b + b x h + h x l) = 2 (15 x 10 + 10 x 8 + 8 x 15) = 
2(150 + 80 +120) = 2 x 350 = 700 cm
2
 
(ii) Length = 3.5 m Breadth = 2.6 m, Height = 90 cm =  m = 0.9 m. 
Volume of a cuboid = l x b x h = 3.5 x 2.6 x 0.9 = 8.19 m
3
 
Total surface area of a cuboid = 2(l x b + b x h + h x l) 
= 2 (3.5 x 2.6 + 2.6 x 0.9 + 0.9 x 3.5) = 2 (910 + 2.34 + 3.15) = 2(14.59)= 29.18 m
2
 
Question 2. 
(i) The volume of a cuboid is 3456 cm
3
. If its length = 24 cm and breadth = 18 cm ; find 
its height. 
(ii) The volume of a cuboid is 7.68 m
3
. If its length = 3.2 m and height = 1.0 m; find its 
breadth. 
(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If 
the volume of the cuboid is 1.92 m
3
; find its length. 
Solution: 
(i) Volume of the given cuboid = 3456 cm
3
. 
Length of the given cuboid = 24 cm. 
Breadth of the given cuboid = 18 cm 
We know, 
Length x Breadth x Height = Volume of a cuboid 
? 24 x 18 x Height = 3456 
? Height =  
? Height =  
? Height = 8 cm 
(ii) Volume of a cuboid = 7.68 m
3
 
Length of a cuboid = 3.2 m 
Height of a cuboid = 10m 
We know 
Length x Breadth x Height = Volume of a cuboid 
3.2 x Breadth x 1.0 = 7.68 
? Breadth =  
? Breadth =  
? Breadth = 2.4 m 
(iii) Volume of a rectangular solid = 1.92 m
3
 
Breadth of a rectangular solid = 1.20 m 
Height of a rectangular solid = 80 cm = 0.8 m 
We know 
Length x Breadth x Height = Volume of a rectangular solid (cubical) 
Length x 1.20 x 0.8 = 1.92 
Length x 0.96 = 1.92 
? Length =  
? Length =  
? Length = 2 m 
Question 3. 
The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 
cm
3
; find its dimensions. (Dimensions means : its length, breadth and height). Also find 
the total surface area of the cuboid. 
Solution: 
Let length of the given cuboid = 5x 
Breadth of the given cuboid = 3x 
Height of the given cuboid = 2x 
Volume of the given cuboid = Length x Breadth x Height 
= 5x x 3x x 2x = 30x
3
 
But we are given volume = 240 cm
3
 
30x
3
 = 240 cm
3
 
? x
3
 =  
? x
3
 = 8 
? x =  
? x =  
? x = 2 cm 
Length of the given cube = 5x = 5 x 2 = 10 cm 
Breadth of the given cube = 3x = 3 x 2 = 6 cm 
Height of the given cube = 2x = 2 x 2 = 4cm 
Total surface area of the given cuboid = 2(l x b + b x h + h x l) 
= 2(10 x 6 + 6 x 4 + 4 x 10) = 2(60 + 24 + 40) = 2 x 124 = 248 cm
2
 
Question 4. 
The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface 
area is 504 cm2; find its dimensions. Also, find the volume of the cuboid. 
Solution: 
Let length of the cuboid = 6x 
Breadth of the cuboid = 5x 
Height of the cuboid = 3x 
Total surface area of the given cuboid = 2 (I x b + b x h + h x l) 
= 2(6x x 5x + 5x x 3x + 3x x 6x) = 2(30×2 + 15×2 + 18×2) 
= 2 x 63×2 = 126x
2
 
But we are given total surface area of the given cuboid = 504 cm
2
 
126x
2
 = 504 cm
2
 
=> x
2
 =  
=> x
2
 = 4 
=> x = v4 
=> x = 2 cm. 
Length of the cuboid = 6x = 6 x 2 = 12 cm 
Breadth of the cuboid = 5x = 5 x 2 = 10cm 
Height of the cuboid = 3x = 3 x 2 = 6 cm 
Volume of the cuboid = l x b x h = 12 x 10 x 6 = 720 cm
3
 
Question 5. 
Find the volume and total surface area of a cube whose each edge is : 
(i) 8 cm 
(ii) 2 m 40 cm. 
Solution: 
(i) Edge of the given cube = 8 cm 
Volume of the given cube = (Edge)
3
 = (8)
3
 = 8 x 8 x 8 = 512 cm
3
 
Total surface area of a cube = 6(Edge)
2
 = 6 x (8)
2
 = 384 cm
2
 
(ii) Edge of the given cube = 2 m 40 cm = 2.40 m 
Volume of a cube = (Edge)
3
 
Volume of the given cube = (2.40)
3
 = 2.40 x 2.40 x 2.40 = 13.824 m
2
 
Total surface area of the given cube = 6 x 2.4 x 2.4 = 34.56 m
2
 
Question 6. 
Find the length of each edge of a cube, if its volume is : 
(i) 216 cm
3
 
(ii) 1.728 m
3
 
Solution: 
 
Question 7. 
The total surface area of a cube is 216 cm2. Find its volume. 
Solution: 
6(Edge)
2
 = Total surface area of a cube 
6(Edge)
2
 = 216 cm
2
 
=> (Edge)
2
 =  
=> (Edge)
2
 = 36 
=> Edge = v36 
=> Edge = 6 cm 
Volume of the given cube = (Edge)
3
 = (6)
3
 = 6 x 6 x 6 = 216 cm
3
 
Question 8. 
A solid cuboid of metal has dimensions 24 cm, 18 cm and 4 cm. Find its volume. 
Solution: 
Length of the cuboid = 24 cm 
Breadth of the cuboid = 18 cm 
Page 5


21. Surface Area, Volume and Capacity  
(Cuboid, Cube and Cylinder) 
EXERCISE 21 (A) 
Question 1. 
Find the volume and the total surface area of a cuboid, whose : 
(i) length = 15 cm, breadth = 10 cm and height = 8 cm. 
(ii) l = 3.5 m, b = 2.6 m and h = 90 cm, 
Solution: 
(i) Length =15 cm, Breadth = 10 cm, Height = 8 cm. 
Volume of a cuboid = Length x Breadth x Height = 15 x 10 x 8 =1200 cm
3
. 
Total surface area of a cuboid 2 (l x b + b x h + h x l) = 2 (15 x 10 + 10 x 8 + 8 x 15) = 
2(150 + 80 +120) = 2 x 350 = 700 cm
2
 
(ii) Length = 3.5 m Breadth = 2.6 m, Height = 90 cm =  m = 0.9 m. 
Volume of a cuboid = l x b x h = 3.5 x 2.6 x 0.9 = 8.19 m
3
 
Total surface area of a cuboid = 2(l x b + b x h + h x l) 
= 2 (3.5 x 2.6 + 2.6 x 0.9 + 0.9 x 3.5) = 2 (910 + 2.34 + 3.15) = 2(14.59)= 29.18 m
2
 
Question 2. 
(i) The volume of a cuboid is 3456 cm
3
. If its length = 24 cm and breadth = 18 cm ; find 
its height. 
(ii) The volume of a cuboid is 7.68 m
3
. If its length = 3.2 m and height = 1.0 m; find its 
breadth. 
(iii) The breadth and height of a rectangular solid are 1.20 m and 80 cm respectively. If 
the volume of the cuboid is 1.92 m
3
; find its length. 
Solution: 
(i) Volume of the given cuboid = 3456 cm
3
. 
Length of the given cuboid = 24 cm. 
Breadth of the given cuboid = 18 cm 
We know, 
Length x Breadth x Height = Volume of a cuboid 
? 24 x 18 x Height = 3456 
? Height =  
? Height =  
? Height = 8 cm 
(ii) Volume of a cuboid = 7.68 m
3
 
Length of a cuboid = 3.2 m 
Height of a cuboid = 10m 
We know 
Length x Breadth x Height = Volume of a cuboid 
3.2 x Breadth x 1.0 = 7.68 
? Breadth =  
? Breadth =  
? Breadth = 2.4 m 
(iii) Volume of a rectangular solid = 1.92 m
3
 
Breadth of a rectangular solid = 1.20 m 
Height of a rectangular solid = 80 cm = 0.8 m 
We know 
Length x Breadth x Height = Volume of a rectangular solid (cubical) 
Length x 1.20 x 0.8 = 1.92 
Length x 0.96 = 1.92 
? Length =  
? Length =  
? Length = 2 m 
Question 3. 
The length, breadth and height of a cuboid are in the ratio 5 : 3 : 2. If its volume is 240 
cm
3
; find its dimensions. (Dimensions means : its length, breadth and height). Also find 
the total surface area of the cuboid. 
Solution: 
Let length of the given cuboid = 5x 
Breadth of the given cuboid = 3x 
Height of the given cuboid = 2x 
Volume of the given cuboid = Length x Breadth x Height 
= 5x x 3x x 2x = 30x
3
 
But we are given volume = 240 cm
3
 
30x
3
 = 240 cm
3
 
? x
3
 =  
? x
3
 = 8 
? x =  
? x =  
? x = 2 cm 
Length of the given cube = 5x = 5 x 2 = 10 cm 
Breadth of the given cube = 3x = 3 x 2 = 6 cm 
Height of the given cube = 2x = 2 x 2 = 4cm 
Total surface area of the given cuboid = 2(l x b + b x h + h x l) 
= 2(10 x 6 + 6 x 4 + 4 x 10) = 2(60 + 24 + 40) = 2 x 124 = 248 cm
2
 
Question 4. 
The length, breadth and height of a cuboid are in the ratio 6 : 5 : 3. If its total surface 
area is 504 cm2; find its dimensions. Also, find the volume of the cuboid. 
Solution: 
Let length of the cuboid = 6x 
Breadth of the cuboid = 5x 
Height of the cuboid = 3x 
Total surface area of the given cuboid = 2 (I x b + b x h + h x l) 
= 2(6x x 5x + 5x x 3x + 3x x 6x) = 2(30×2 + 15×2 + 18×2) 
= 2 x 63×2 = 126x
2
 
But we are given total surface area of the given cuboid = 504 cm
2
 
126x
2
 = 504 cm
2
 
=> x
2
 =  
=> x
2
 = 4 
=> x = v4 
=> x = 2 cm. 
Length of the cuboid = 6x = 6 x 2 = 12 cm 
Breadth of the cuboid = 5x = 5 x 2 = 10cm 
Height of the cuboid = 3x = 3 x 2 = 6 cm 
Volume of the cuboid = l x b x h = 12 x 10 x 6 = 720 cm
3
 
Question 5. 
Find the volume and total surface area of a cube whose each edge is : 
(i) 8 cm 
(ii) 2 m 40 cm. 
Solution: 
(i) Edge of the given cube = 8 cm 
Volume of the given cube = (Edge)
3
 = (8)
3
 = 8 x 8 x 8 = 512 cm
3
 
Total surface area of a cube = 6(Edge)
2
 = 6 x (8)
2
 = 384 cm
2
 
(ii) Edge of the given cube = 2 m 40 cm = 2.40 m 
Volume of a cube = (Edge)
3
 
Volume of the given cube = (2.40)
3
 = 2.40 x 2.40 x 2.40 = 13.824 m
2
 
Total surface area of the given cube = 6 x 2.4 x 2.4 = 34.56 m
2
 
Question 6. 
Find the length of each edge of a cube, if its volume is : 
(i) 216 cm
3
 
(ii) 1.728 m
3
 
Solution: 
 
Question 7. 
The total surface area of a cube is 216 cm2. Find its volume. 
Solution: 
6(Edge)
2
 = Total surface area of a cube 
6(Edge)
2
 = 216 cm
2
 
=> (Edge)
2
 =  
=> (Edge)
2
 = 36 
=> Edge = v36 
=> Edge = 6 cm 
Volume of the given cube = (Edge)
3
 = (6)
3
 = 6 x 6 x 6 = 216 cm
3
 
Question 8. 
A solid cuboid of metal has dimensions 24 cm, 18 cm and 4 cm. Find its volume. 
Solution: 
Length of the cuboid = 24 cm 
Breadth of the cuboid = 18 cm 
Height of the cuboid = 4 cm 
Volume of the cuboid = l x b x h = 24 x 18 x 4 = 1728 cm
3
 
Question 9. 
A wall 9 m long, 6 m high and 20 cm thick, is to be constructed using bricks of 
dimensions 30 cm, 15 cm and 10 cm. How many bricks will be required. 
Solution: 
Length of the wall = 9 m = 9 x 100 cm = 900 cm 
Height of the wall = 6 m = 6 x 100 cm = 600 cm 
Breadth of the wall = 20 cm 
Volume of the wall = 900 x 600 x 20 cm3 = 10800000 cm
3
 
Volume of one Brick = 30 x 15 x 10 cm
3
 = 4500 cm
3
 
Number of bricks required to construct the wall =  
=  
= 2400 
Question 10. 
A solid cube of edge 14 cm is melted down and recasted into smaller and equal cubes 
each of edge 2 cm; find the number of smaller cubes obtained. 
Solution: 
Edge of the big solid cube = 14 cm 
Volume of the big solid cube = 14 x 14 x 14 cm3 = 2744 cm
3
 
Edge of the small cube = 2 cm 
Volume of one small cube = 2 x 2 x 2 cm
3
 = 8 cm
3
 
Number of smaller cubes obtained =  
=  = 343 
Question 11. 
A closed box is cuboid in shape with length = 40 cm, breadth = 30 cm and height = 50 
cm. It is made of thin metal sheet. Find the cost of metal sheet required to make 20 
such boxes, if 1 m
2
 of metal sheet costs Rs. 45. 
Solution: 
Length of closed box (l) = 40 cm 
Breadth (b) = 30 cm 
and height (h) = 50 cm