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
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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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