How many balls, each of radius 1 cm, can be made from a steel sphere whose radius is 6 cm?

Options

A. 126
B. 27
C. 64
D. 216

Answer

To solve the problem of how many balls, each of radius 1 cm, can be made from a steel sphere whose radius is 6 cm, we will follow these steps:

### Step 1: Calculate the volume of the steel sphere.
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi R^3 \]
where \( R \) is the radius of the sphere. Here, the radius of the steel sphere is 6 cm.

Substituting the value of \( R \):
\[ V = \frac{4}{3} \pi (6)^3 \]
Calculating \( 6^3 \):
\[ 6^3 = 216 \]
Now substituting back into the volume formula:
\[ V = \frac{4}{3} \pi (216) = \frac{864}{3} \pi = 288 \pi \text{ cubic centimeters} \]

### Step 2: Calculate the volume of one ball.
Using the same volume formula for the smaller balls, where the radius \( r \) is 1 cm:
\[ v = \frac{4}{3} \pi (1)^3 \]
Calculating \( 1^3 \):
\[ 1^3 = 1 \]
Now substituting back into the volume formula:
\[ v = \frac{4}{3} \pi (1) = \frac{4}{3} \pi \text{ cubic centimeters} \]

### Step 3: Determine how many balls can be made from the steel sphere.
To find the number of balls that can be made, we divide the volume of the steel sphere by the volume of one ball:
\[ \text{Number of balls} = \frac{\text{Volume of steel sphere}}{\text{Volume of one ball}} = \frac{288 \pi}{\frac{4}{3} \pi} \]
The \( \pi \) cancels out:
\[ \text{Number of balls} = \frac{288}{\frac{4}{3}} = 288 \times \frac{3}{4} = 216 \]

### Conclusion:
Thus, the number of balls that can be made from the steel sphere is **216**.

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