How many cuboids of sides 3 cm, 6 cm and 5 cm are needed to form a cube!
Answers
Answer:
300 cuboids are needed to form a cube.
Step-by-step explanation:
Given:
- Sides of each cuboid are 3 cm, 6 cm and 5 cm respectively.
To find:
- How many cuboids are needed to form a cube.
Solution:
♦ Volume of a cuboid = l × b × h
Where,
l is the length of a cuboid.
b is the breadth of a cuboid.
h is the height of a cuboid.
Putting the values in the formula, we have:
- Volume of a cuboid = 3 × 6 × 5
- Volume of a cuboid = 3 × 30
- Volume of a cuboid = 90 cm³
Now, the length of one side of a cube is equal to L.C.M of 3, 6 and 5 which is 30.
♦ Volume of a cube = a³
Where,
a is the length of one side of a cube.
Putting the values in the formula, we have:
- Volume of a larger cube = 30³
- Volume of a larger cube = 30 × 30 × 30
- Volume of a larger cube = 900 × 30
- Volume of a larger cube = 27000 cm³
Finally,
- Number of cuboids needed = Volume of a larger cube/Volume of a cuboid
- Number of cuboids needed = 27000/90
- Number of cuboids needed = 2700/9
- Number of cuboids needed = 300
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Step-by-step explanation:
Solution:
♦ Volume of a cuboid = l × b × h
Where,
l is the length of a cuboid.
b is the breadth of a cuboid.
h is the height of a cuboid.
Putting the values in the formula, we have:
Volume of a cuboid = 3 × 6 × 5
Volume of a cuboid = 3 × 30
Volume of a cuboid = 90 cm³
Now, the length of one side of a cube is equal to L.C.M of 3, 6 and 5 which is 30.
♦ Volume of a cube = a³
Where,
a is the length of one side of a cube.
Putting the values in the formula, we have:
Volume of a larger cube = 30³
Volume of a larger cube = 30 × 30 × 30
Volume of a larger cube = 900 × 30
Volume of a larger cube = 27000 cm³
Finally,
Number of cuboids needed = Volume of a larger cube/Volume of a cuboid
Number of cuboids needed = 27000/90
Number of cuboids needed = 2700/9
Number of cuboids needed = 300
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