Question : A cuboid is of dimensions 80 cm × 64 cm × 50 cm How many small cubes with sides 8 cm can be placed in the given cuboid?
Option 1: 480
Option 2: 700
Option 3: 1000
Option 4: 200
Correct Answer: 480
Solution :
Length of cuboid, $l$ = 80 cm
Breadth of cuboid, $b$ = 64 cm
Height of cuboid, $h$ = 50 cm
Side of a cube, $a$ = 8 cm
But height, $h$ should be multiple of $a$.
Here, Height utilised = 50 – 2 = 48 cm
Let $n$ be the number of cubes.
The volume of a cuboid = number of cubes × volume of a cube
$l×b×h=n × a^3$
$⇒80 × 64 × 48=n × 8 × 8 × 8$
$⇒n=\frac{80 × 64 × 48}{8 × 8 × 8}$
$\therefore n = 480$
Hence, the correct answer is 480.
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