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
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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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