A spherical ball of radius 3 cm contains 66.66% iron. If density of ball is 1.5 g/`cm^3` then the number of mole of Fe present approximately is:

Options

A. 1
B. 2
C. 20
D. 10

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the Volume of the Spherical 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. Given that the radius \( r = 3 \) cm:

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

Calculating \( (3)^3 = 27 \):

\[ V = \frac{4}{3} \pi (27) = 36 \pi \text{ cm}^3 \]

Using \( \pi \approx 3.14 \):

\[ V \approx 36 \times 3.14 \approx 113.097 \text{ cm}^3 \]

### Step 2: Calculate the Mass of the Spherical Ball
Using the density formula:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Rearranging gives us:

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

Given the density is \( 1.5 \text{ g/cm}^3 \):

\[ \text{Mass} = 1.5 \text{ g/cm}^3 \times 113.097 \text{ cm}^3 \approx 169.6455 \text{ g} \]

### Step 3: Calculate the Mass of Iron in the Ball
The ball contains \( 66.66\% \) iron. Therefore, the mass of iron can be calculated as follows:

\[ \text{Mass of Iron} = \text{Total Mass} \times \frac{66.66}{100} \]

\[ \text{Mass of Iron} = 169.6455 \text{ g} \times 0.6666 \approx 113.097 \text{ g} \]

### Step 4: Calculate the Number of Moles of Iron
To find the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

The molar mass of iron \( (Fe) \) is approximately \( 56 \text{ g/mol} \):

\[ \text{Number of moles of Fe} = \frac{113.097 \text{ g}}{56 \text{ g/mol}} \approx 2.01 \text{ moles} \]

### Conclusion
The number of moles of iron present in the spherical ball is approximately \( 2.01 \), which can be rounded to \( 2 \).

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