A cuboid measures 36 mx 24 mx 18 m. How many cubes of edge 6 m can be cut from the cuboid?
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Answer:
72 cubes of edge 6 m can be cut from the cuboid.
Step-by-step-explanation:
We have given that,
For a cuboid,
- Length ( L ) = 36 m
- Breadth ( B ) = 24 m
- Height ( H ) = 18 m
For a cube,
- Edge ( l ) = 6 m
We have to find the number of cubes which can be cut from the cuboid.
The number of cubes required to make the sum of volumes of each cube with equal edges equal to the volume of the cuboid is required number of cubes which can be cut from the cuboid.
∴ Volume of cube 1 + Volume of cube 2 + Volume of cube 3 + .... Volume of cube n = Volume of cuboid
We know that,
- Volume of cube = ( Length of edge )³
- Volume of cuboid = Length * Breadth * Height
⇒ l³ + l³ + l³ + .... l³ n times = L * B * H
⇒ l³ * n = LBH
⇒ n = LBH/l³
⇒ n = ( 36 * 24 * 18 ) / 6³
⇒ n = ( 36 * 24 * 18 ) / ( 6 * 6 * 6 )
⇒ n = 36 ÷ 6 * 24 ÷ 6 * 18 ÷ 6
⇒ n = 6 * 4 * 3
⇒ n = 24 * 3
⇒ n = 72
∴ 72 cubes of edge 6 m can be cut from the cuboid.
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