If the length, width and height of a cuboid are l, w and h respectively, then
volume of the cuboid = l x w x h cubic units
Problem 1 :
The length, breadth and depth of a pond are 20.5 m, 16 m and 8 m respectively. Find the capacity of the pond in liters.
Solution :
l = 20.5 m, w = 16 m, h = 8 m
Capacity of pond :
= l x w x h
= 20.5 (16) (8)
= 2624 m^{3}
1 m^{3 }= 1000 liters
= 2624(1000) liters
= 2624000 liters
Problem 2 :
The dimensions of a brick are 24 cm x 12 cm x 8 cm. How many such bricks will be required to build a wall of 20 m length, 48 cm breadth and 6 m height?
Solution :
Volume of 1 brick :
= l x w x h
= 24(12)(8)
= 2304 cm^{3}
Dimensions of the wall :
l = 20 m = 2000 cm
w = 48 cm
h = 6 m = 6000 cm
Volume of wall :
= l x w x h
= 2000(48)(600)
= 57600000 cm^{3}
Number of bricks required :
= 57600000/2304
= 25000
Problem 3 :
The volume of a container is 1440 m^{3}. The length and width of the container are 15 m and 8 m respectively. Find its height
Solution :
Volume of container = 1440 m^{3}
length x width x height = 1440
15 x 8 x h = 1440
height = 1440/120
height = 12 m
Problem 4 :
The side of a metallic cube is 12 in. It is melted and formed into a cuboid whose length and width are 18 in and 16 cm respectively. Find the height of the cuboid.
Solution :
volume of cuboid = volume of cube
l x w x h = a^{3}
18 x 16 x h = 12^{3}
288h = 1728
Divide both sides by 288.
h = 6 in
Problem 5 :
The length, width and height of a cuboid are in the ratio 7 : 5 : 2. Its volume is 35840 cm3. Find its dimensions.
Solution :
From the ratio 7 : 5 : 2, the dimensions of the cuboid are
length = 7x, width = 5x, height = 2x
Volume = 35840 cm^{3}
(7x)(5x)(2x) = 35840
70x^{3} = 35840
Divide each side by 70.
x^{3} = 512
x^{3} = 8^{3}
x = 8
Length = 7(8) = 56 cm
Width = 5(8) = 40 cm
Height = 2(8) = 16 cm
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