how many cuboids of side 3 cm 6 cm and 5 cm are needed to form a cube
Answers
Volume of cuboid = lbh
=6*5*3
=90 cm^3
Volume of cube=side*side*side
Side would have been given to you.
Now divide the volume of cube by volume of cuboid=90
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Number of cuboids required to form a cube = 300
Given:
Sides of cuboid 3 cm 6 cm and 5 cm
To find:
Number of cuboids needed to form a cube
Solution:
Given dimensions of cuboid = 3 cm × 6 cm × 5 cm
Volume of cuboid = length × width × height
= 3 × 6 × 5 = 90 cm³
Let n be the number of cuboids that are used to form a cube
then volume of the resultant cube = n × 90 cm³
As we know volume of the cube = side³
Let a be the side of resultant cube
Volume of cube = a³ [ which is equals to n × 90 cm³ ]
⇒ a³ = n × 90 cm³
As we observed a³ is a perfect cube number then (n × 90) will also be a perfect cube number
So, find n value as such that (n × 90) is a perfect cube number
We can find n value as given below
write (n × 90) as product of prime number
(n × 90) = 2 × 3 × 3 × 5 × n
[ none of the factors are in form of a³ ]
Here to get perfect cube number from 90 we need two 2's and one 3 and two 5's
(n × 90) = 2 × 3 × 3 × 5 × 2 × 2 × 3 × 5 × 5 = 27000
(n × 90) = 27000 [ 27000 is perfect cube number as 30³ = 27000 ]
n = 27000/90 = 300
n = 300
Therefore,
Number of cuboids required to form a cube = 300
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