यदि एक घनाभ को 6 cm भुजा वाले घनोसे भरा जाता है तब कुल भरे जाने वाले घनो की संख्या ज्ञात कीजिए जबकि धनाभ की विमाए`60 xx 120 xx 30 cm` दी गई है -

Options

A. 100
B. 1000
C. 200
D. 50

Answer

**Step-by-Step Solution:**

1. **Identify the dimensions of the cuboid:**
- Length (L) = 60 cm
- Width (B) = 120 cm
- Height (H) = 30 cm

2. **Calculate the volume of the cuboid:**
- The formula for the volume of a cuboid is:
\[ \text{Volume of cuboid} = L \times B \times H \]
- Substituting the values:
\[ \text{Volume of cuboid} = 60 \, \text{cm} \times 120 \, \text{cm} \times 30 \, \text{cm} \]
- Calculating:
\[ \text{Volume of cuboid} = 60 \times 120 = 7200 \, \text{cm}^2 \]
\[ \text{Volume of cuboid} = 7200 \times 30 = 216000 \, \text{cm}^3 \]

3. **Calculate the volume of one cube:**
- Given that the side of the cube is 6 cm, the volume of one cube is:
\[ \text{Volume of one cube} = \text{side}^3 = 6 \, \text{cm} \times 6 \, \text{cm} \times 6 \, \text{cm} \]
- Calculating:
\[ \text{Volume of one cube} = 6^3 = 216 \, \text{cm}^3 \]

4. **Calculate the total number of cubes that can fit in the cuboid:**
- The total number of cubes (n) is given by the formula:
\[ n = \frac{\text{Volume of cuboid}}{\text{Volume of one cube}} \]
- Substituting the values:
\[ n = \frac{216000 \, \text{cm}^3}{216 \, \text{cm}^3} \]
- Calculating:
\[ n = 1000 \]

5. **Conclusion:**
- The total number of cubes that can fit in the cuboid is **1000**.

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