Question

A cuboid is of dimensions 30 cm × 24 cm × 20 cm. How many small cubes with side 4 cm can be placed in the given cuboid​

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• Dimensions of the cuboid: Length = 30 cm, Breadth = 24 cm and Height = 20 cm.
• Dimensions of a cube: Side = 4 cm.

${\underline{\underline{\bf{Need\:to\: find:}}}}$

• The number of cubes of above dimensions can be placed inside the cuboid.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Volume}_{(Cuboid)}=lbh\:cu.units}}}$

$\:\:\:\:\:\:\:\:\:\:\bullet{\sf{\:l=length}}$

$\:\:\:\:\:\:\:\:\:\:\bullet{\sf{\:b=breadth}}$

$\:\:\:\:\:\:\:\:\:\:\bullet{\sf{\:h=height}}$

$\underline{\boxed{\sf{{Volume}_{(Cube)}={a}^{3}\:cu.units}}}$

$\:\:\:\:\:\:\:\:\:\:\bullet{\sf{\:a=side}}$

${\underline{\underline{\bf{Solution:}}}}$

The number of cubes that can be placed in the cuboid can be found by dividing the volume of cube from volume of cuboid. So, first we've to find the volume of cuboid, then the cube, finally dividing each other gives the required answer.

Volume of Cuboid:

$\:\:\:\:\:\:\:\:\implies{\sf{lbh\:cu.units}}$

$\:\:\:\:\:\:\:\:\implies{\sf{30\times 24\times 20}}$

$\:\:\:\:\:\:\:\:\implies{\sf{720\times 20}}$

$\:\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{14,400\:{cm}^{3}}}}}$

Volume of Cube:

$\:\:\:\:\:\:\:\:\implies{\sf{{a}^{3}\:cu.units}}$

$\:\:\:\:\:\:\:\:\implies{\sf{{4}^{3}}}$

$\:\:\:\:\:\:\:\:\implies{\sf{4\times 4\times 4}}$

$\:\:\:\:\:\:\:\:\implies{\sf{16\times 4}}$

$\:\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{64\:{cm}^{3}}}}}$

★ Number of cubes that can be placed:

$\:\:\:\:\:\:\:\:\:\:\:\:\:{\boxed{\sf{\frac{Volume\:of\:cuboid}{Volume\:of\:cube}}}}$

By substituting the obtained measures,

$\longrightarrow{\sf{\frac{14400}{64}}}$

$\longrightarrow{\sf{\red{\underline{\underline{225}}}}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• 225 cubes can be placed inside the cuboid of given dimensions.

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