A hollow spherical shell is made of metal of density 4.8 g/`cm^(3)`, If its internal and external radii are 10 cm and 12 cm respectively, find the weight of the shell

Options

A. 15.24 kg
B. 12.84 kg
C. 14.64 kg
D. None of these

Answer

To find the weight of the hollow spherical shell, we will follow these steps:

### Step 1: Identify the given values
- Internal radius (r) = 10 cm
- External radius (R) = 12 cm
- Density (d) = 4.8 g/cm³

### Step 2: Calculate the volume of the hollow spherical shell
The volume \( V \) of a hollow spherical shell can be calculated using the formula:

\[ V = \frac{4}{3} \pi (R^3 - r^3) \]

### Step 3: Substitute the values into the volume formula
Substituting the values of \( R \) and \( r \):

\[ V = \frac{4}{3} \pi (12^3 - 10^3) \]

Calculating \( 12^3 \) and \( 10^3 \):

\[ 12^3 = 1728 \quad \text{and} \quad 10^3 = 1000 \]

Now, substituting these values:

\[ V = \frac{4}{3} \pi (1728 - 1000) \]

Calculating the difference:

\[ 1728 - 1000 = 728 \]

So, we have:

\[ V = \frac{4}{3} \pi (728) \]

### Step 4: Calculate the volume using the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):

\[ V = \frac{4}{3} \times \frac{22}{7} \times 728 \]

### Step 5: Simplify the volume calculation
Calculating:

\[ V = \frac{4 \times 22 \times 728}{3 \times 7} \]

Calculating \( 4 \times 22 = 88 \):

\[ V = \frac{88 \times 728}{21} \]

Calculating \( 88 \times 728 = 64064 \):

\[ V = \frac{64064}{21} \approx 3041.14 \, \text{cm}^3 \]

### Step 6: Calculate the weight of the shell
Weight \( W \) is calculated using the formula:

\[ W = \text{Density} \times \text{Volume} \]

Substituting the values:

\[ W = 4.8 \, \text{g/cm}^3 \times 3041.14 \, \text{cm}^3 \]

Calculating the weight:

\[ W \approx 14596.51 \, \text{g} \]

### Step 7: Convert grams to kilograms
To convert grams to kilograms:

\[ W = \frac{14596.51}{1000} \approx 14.60 \, \text{kg} \]

### Final Answer
The weight of the hollow spherical shell is approximately **14.60 kg**.

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