Cuboid is a solid box whose every surface is a rectangle of same area or different areas.
A cuboid will have a length, breadth and height.
Hence we can conclude that volume is 3 dimensional. To measure the volumes we need to know the measure 3 sides.
Since volume involves 3 sides it is measured in cubic units.
Volume of a cuboid = (length × breadth × height) cubic units.
= (l × b × h) cubic units.
(Since area = ℓ × b)
Volume of a cuboid = area of one surface × height cubic units
Let us look at the given cuboid.
The length of the cuboid = 5 cm
The breadth of the cuboid = 3 cm
The height of cuboid (thickness) = 2 cm
The number of 1 cm cubes in the given cuboid = 30 cubes = 5 × 3 × 2
We find that volume of the given cuboid with length 5 cm, breadth 3 cm and height 2 cm is 30 cu cm.
Therefore, volume of a cuboid = length × breadth × height
Solved examples on volume of a cuboid:
1. Find the volume of a cuboid of dimensions 14 cm × 12 cm × 8 cm.
Solution:
Volume of cuboid = length × breadth × height.
Here, length = 14 cm, breadth = 12 cm and height = 8 cm.
Volume of cuboid = 14 × 12 × 8 cubic cm.
= 1344 cubic cm.
Therefore, volume of cuboid = 1344 cubic cm.
2. Michael made a shoe box with length 8 cm, breadth 6 cm and height 6 cm. Find the volume of the box.
Solution:
Volume of the shoe box = Length × breadth × height.
= 8 × 6 × 6
= 288 cu cm.
3. A fish tank is 40 cm long, 15 cm broad and 10 cm high. What is its volume in cu cm?
Solution:
The length of the fish tank = 40 cm
The breadth of the fish tank = 15 cm
The height of the fish tank = 10 cm
Therefore, the volume of the fish tank = length × breadth × height.
= 40 × 15 × 10 cu. cm
= 6000 cu cm.
4. Find the volume of a cuboid of dimensions 14 cm × 50 mm × 10 cm.
Solution:
Here, length = 14 cm,
[Given,
breadth = 50 mm; we need to convert breadth to same unit and then
solve. We know, 10 mm = 1 cm. Therefore, 50 mm = 50/10 cm = 5 cm].
Breadth = 5 cm,
Height = 10 cm.
Volume of cuboid = length × breadth × height.
= 14 × 5 × 10
= 700 cubic cm.
Therefore, volume of cuboid = 700 cubic cm.
Note: In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and then solve.
5. Find the volume of a cuboid of dimensions 17 mm × 0.2 cm × 12 mm in cu. cm.
Solution:
Given, length = 17 mm.
We know, 10 mm = 1 cm.
= 17/10 cm.
= 1.7 cm.
Therefore, length = 1.7 cm.
Similarly, height = 12 mm.
We know, 10 mm = 1 cm.
= 12/10 cm.
= 1.2 cm.
Therefore, height = 1.2 cm.
Volume of cuboid = length × breadth × height.
Length = 1.7 cm, breadth = 0.2 cm and height = 1.2 cm.
= 1.7 × 0.2 × 1.2 cu. cm.
= 0.408 cu. cm.
Therefore, volume of cuboid = 0.408 cubic cm.
6. Find the number of cubical boxes of cubical side 3 cm which can be accommodated in carton of dimensions 15 cm × 9 cm × 12 cm.
Solution:
Volume of box = side × side × side.
= 3 × 3 × 3
= 27 cu. cm.
Volume of carton = length × breadth × height.
= 15 × 9 × 12
= 1620 cu. cm.
Number of boxes = Volume of carton/Volume of each box.
= 1620/27
= 60
Therefore, number of cubical boxes = 60.
7. How many bricks each 25 cm long, 10 cm wide and 7.5 cm thick will be required for a wall 20 m long, 2 m high and 0.75 m thick? If bricks sell at $900 per thousand what will it cost to build the wall?
Solution:
Volume of the wall = 20 m × 2 m × 0.75 m
= 20 × 100 cm × 2 × 100 cm × 0.75 × 100 cm
Volume of brick = 25 cm × 10 cm × 7.5 cm
Number of bricks = Volume of the wall/Volume of the brick
= 20 × 100 × 2 × 100 × 0.75 × 100/25 × 10 × 7.5
= 16000
The number of bricks = 16000
The cost of 1 thousand bricks = $ 900
The cost of building the wall = $ 900 × 16 = $ 14400
Note: While calculating the volume of a cuboid all the dimensions should be changed into the same unit.
Questions and Answers on Cuboid:
1. Find the volume of each of the cuboids.
(i) Length = 5 cm, Breadth = 4 cm and Height = 3 cm
(ii) Length = 15 m, Breadth = 10 m and Height = 2 m
(iii) Length = 0.5 m, Breadth = 3 m and Height = 4 m
(iv) Length = 3.2 cm, Breadth = 2 cm and Height = 8 cm
(v) Length = 5 m, Breadth = 1.5 m and Height = 1.2 m
Answers:
1. (i) 60 cu cm
(ii) 300 cu m
(iii) 6 cu m
(iv) 51.2 cu cm
(v) 9 cu m
2. Find the volume of these tanks.
(i) Length = 16 cm, Breadth = 60 cm and Height = 20 cm
(ii) Length = 6 m, Breadth = 3 m and Height = 5 m
(iii) Length = 2 m, Breadth = 1.5 m and Height = 1.5 m
(iv) Length = 80 cm, Breadth = 20 cm and Height = 40 cm
(v) Length = 1.2 m, Breadth = 1.2 m and Height = 1 m
Answers:
2. (i) 19200 cu cm
(ii) 90 cu m
(iii) 4.5 cu m
(iv) 64,000 cu cm
(v) 1.44 cu m
● Volume.
5th Grade Geometry
5th Grade Math Problems
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