A spherical lead ball of radius 10 cm is melted and small lead balls of radius 5mm are made. The total number of possible small lead balls is (Take `pi = (22)/(7)`)

Options

A. 8000
B. 400
C. 800
D. 125

Answer

To solve the problem, we need to find the total number of small lead balls that can be made from a larger spherical lead ball after melting it down.

### Step 1: Calculate the volume of the large lead ball
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.

For the large lead ball, the radius \( r = 10 \) cm. Therefore, the volume \( V \) is:
\[ V = \frac{4}{3} \times \frac{22}{7} \times (10)^3 \]

### Step 2: Calculate the volume of the large lead ball
First, calculate \( (10)^3 \):
\[ (10)^3 = 1000 \]
Now substitute this value into the volume formula:
\[ V = \frac{4}{3} \times \frac{22}{7} \times 1000 \]
Now calculate \( \frac{4 \times 22 \times 1000}{3 \times 7} \):
\[ V = \frac{88000}{21} \text{ cm}^3 \]

### Step 3: Calculate the volume of a small lead ball
Now, we calculate the volume of a small lead ball with radius \( r = 5 \) mm. First, convert the radius to centimeters:
\[ 5 \text{ mm} = 0.5 \text{ cm} \]
Now, using the volume formula again:
\[ V_{small} = \frac{4}{3} \pi r^3 \]
Substituting \( r = 0.5 \) cm:
\[ V_{small} = \frac{4}{3} \times \frac{22}{7} \times (0.5)^3 \]
Calculating \( (0.5)^3 \):
\[ (0.5)^3 = 0.125 \]
Now substitute this value into the volume formula:
\[ V_{small} = \frac{4}{3} \times \frac{22}{7} \times 0.125 \]
Now calculate \( \frac{4 \times 22 \times 0.125}{3 \times 7} \):
\[ V_{small} = \frac{11}{21} \text{ cm}^3 \]

### Step 4: Calculate the total number of small lead balls
To find the total number of small lead balls, we divide the volume of the large lead ball by the volume of one small lead ball:
\[ \text{Number of small balls} = \frac{V_{large}}{V_{small}} = \frac{\frac{88000}{21}}{\frac{11}{21}} \]
This simplifies to:
\[ \text{Number of small balls} = \frac{88000}{11} \]
Calculating this gives:
\[ \text{Number of small balls} = 8000 \]

### Final Answer
The total number of small lead balls that can be made is **8000**.

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