Question 13 of 18intermediate🔧 ApplyMCQ2 marks

The length, width, and height of a box are 12 cm, 18 cm, and 36 cm respectively. Which of the following sized cubes can be packed in this box without leaving gaps? (a) 9 cm (b) 6 cm (c) 4 cm (d) 3 cm (e) 2 cm

Exercise: Figure it Out (Section 6) | Q: 15 | (Page Page 18)
For More Understanding

Explanation

For a cube of side 's' to fit perfectly in a box of dimensions 12×1812 \times 18 × 36, 's' must be a common factor of 12, 18, and 36. Finding HCF: 12 = 2² × 3, 18 = 2×32 \times 3², 36 = 2² × 3². HCF = 2×32 \times 3 = 6. So the largest cube that fits has side 6 cm. Any factor of 6 will also work. Factors of 6 are: 1, 2, 3, 6. From the options: 9 cm (not a factor of 12), 6 cm (works), 4 cm (not a factor of 18), 3 cm (works), 2 cm (works).

Solution Steps

  1. Step 1: Find HCF of 12, 18, and 36.

  2. Step 2: HCF = 6, so 6 cm cubes fit perfectly.

  3. Step 3: Any factor of 6 will also work: 1, 2, 3, 6.

  4. Step 4: Check each option: 9 (no), 6 (yes), 4 (no), 3 (yes), 2 (yes).

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