Question : The length of each side of a cube is 24 cm. The volume of the cube is equal to the volume of a cuboid. If the breadth and the height of the cuboid are 32 cm and 12 cm, respectively, then what will be the length of the cuboid?
Option 1: 36 cm
Option 2: 56 cm
Option 3: 48 cm
Option 4: 42 cm
Correct Answer: 36 cm
Solution :
The length of each side of a cube is = 24 cm
The volume of a cube = (Side)
3
= 24
3
= 13824
The breadth of the cuboid, b = 32 cm
The height of the cuboid, h = 12 cm
Let the length be l.
Volume of a cuboid = l × b × h
According to the question,
13824 = l × 32 × 12
⇒ l = $\frac{13824}{32×12}$
$\therefore$ l = 36 cm
Hence, the correct answer is 36 cm.
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