The length breadth and height of a cuboid are 36cm,24cm, and 15cm.respectively. how many cubes of edage 6cm. Can be cut out from this cuboid
Answers
Given that the length,breadth and height of the cuboid are 36 cm, 24 cm and 15 cm respectively. Also, length of edge of cube should be 6 cm.
If we have to find the number of cubes which will be formed from the cuboid of length, breadth and height of 36cm,24cm, and 15cm.respectively.Suppose, if a cubes are formed, product of volume of one cube and the number of cubes will be equal to the total volume of the cuboid.
It simply means that if the number of formed cubes is a,
= > a x volume of one cube = volume of cuboid
We are given with the measurements of the cuboid and cubes ( to be formed ).
Let n cubes of 6 cm will be formed from the cuboid of the given measurements.
From above,
= > number of cubes x volume of one cube = volume of cuboid
= > n x volume of cube of 6 cm = volume of cuboid of length, breadth and height of 36cm,24cm, and 15cm respectively.
From the properties of cuboid and cube : -
- Volume of cuboid = length x breadth x height
- Volume of cube = edge^3
Thus,
= > n x ( 6 cm )^3 = 36 cm x 24 cm x 15 cm
= > n x 6 cm x 6 cm x 6 cm = 6 x 6 cm x 6 x 4 cm x 15 cm
= > n = ( 6 x 6 x 6 x 4 x 15 cm^3 ) / ( 6 x 6 x 6 cm^3 )
= > n = 4 x 15
= > n = 60
Hence, the number of cubes which will form from the cuboid is 60.