A carton is 30 cm long, 15 cm broad and 20 cm high. How many books of size 5 cm by 3 cm by 3 cm can be kept in the carton?
a) 200
b) 300
c) 250
Answers
Answer:
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.
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.
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.
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.
Answer:
Step-1
length of a carton = 30 cm .
Breadth of a carton = 15cm.
Height of the carton = 20cm .
volume = L×B×H
= 30x15x20
= 9,000.cu cm.
Volume = 9,000. cu cm.
Step-2
length of a book = 5 cm.
Breadth of a book = 3cm.
Height of a book = 3cm.
volume of a book = 45 cu cm.
Step-3
volume of the carton =9,000cu cm.
volume of the book = 45 cu cm.
now, divide volume of carton and the book .
= 9,000 ÷45 cu cm.
= 200 .
Hence , 200 books can fit in the carton.