A metal sphere of radius 9 cm is melted and small balls of radius 0.6 cm are being made from it, the number of small balls are :

Question

Accepted Answer

To determine the number of small balls that can be made from a metal sphere, we need to compare the volumes of the original sphere and the small balls. The volume of a sphere is calculated using the formula:

$$ V = \frac{4}{3} \pi r^3 $$

where $ r $ is the radius of the sphere.

1. **Calculate the volume of the original metal sphere:**

The radius of the original sphere is 9 cm. Therefore, its volume is:

$$ V_{\text{original}} = \frac{4}{3} \pi (9)^3 = \frac{4}{3} \pi \times 729 = 972 \pi \, \text{cubic cm} $$

2. **Calculate the volume of one small ball:**

The radius of each small ball is 0.6 cm. Therefore, the volume of one small ball is:

$$ V_{\text{small}} = \frac{4}{3} \pi (0.6)^3 = \frac{4}{3} \pi \times 0.216 = 0.288 \pi \, \text{cubic cm} $$

3. **Determine the number of small balls:**

To find the number of small balls that can be made, divide the volume of the original sphere by the volume of one small ball:

$$ \text{Number of small balls} = \frac{V_{\text{original}}}{V_{\text{small}}} = \frac{972 \pi}{0.288 \pi} = \frac{972}{0.288} = 3375 $$

Thus, the number of small balls that can be made is 3375, which corresponds to Option 3.

**Explanation for why other options are incorrect:**

- **Option 1 (3345):** This number is incorrect because the calculation shows that the exact number of small balls is 3375. The discrepancy arises from incorrect division or rounding errors.

- **Option 2 (3275):** This option is also incorrect for the same reason as Option 1. The precise calculation yields 3375, not 3275.

- **Option 4 (3475):** This option is incorrect because it exceeds the calculated number of 3375. The calculation based on the volume formula does not support this number.

In conclusion, the correct answer is Option 3 (3375), as it accurately reflects the number of small balls that can be made from the original metal sphere based on the volume calculations.