What is the volume of a hollow cylinder open at both ends, if its length is 25 cm, external radius is 10 cm and thickness is 1 cm ?
(Take `pi = (22)/(7)`)

Options

A. 2985.72 cu. Cm
B. 746.43 cu. cm
C. 2239.29 cu. cm
D. 1492.86 cu. cm

Answer

To find the volume of a hollow cylinder open at both ends, we can use the formula for the volume of a hollow cylinder:

\[ \text{Volume} = \pi h (R^2 - r^2) \]

where:
- \( R \) is the external radius,
- \( r \) is the internal radius,
- \( h \) is the height (length) of the cylinder.

### Step 1: Identify the given values
- Length (height) of the cylinder, \( h = 25 \) cm
- External radius, \( R = 10 \) cm
- Thickness of the cylinder = 1 cm

### Step 2: Calculate the internal radius
The internal radius \( r \) can be calculated by subtracting the thickness from the external radius:

\[ r = R - \text{thickness} = 10 \, \text{cm} - 1 \, \text{cm} = 9 \, \text{cm} \]

### Step 3: Substitute the values into the volume formula
Now we can substitute \( R \), \( r \), and \( h \) into the volume formula:

\[ \text{Volume} = \pi h (R^2 - r^2) \]

Substituting the values:

\[ \text{Volume} = \frac{22}{7} \times 25 \times (10^2 - 9^2) \]

### Step 4: Calculate \( R^2 - r^2 \)
Now calculate \( R^2 \) and \( r^2 \):

\[ R^2 = 10^2 = 100 \]
\[ r^2 = 9^2 = 81 \]

Thus,

\[ R^2 - r^2 = 100 - 81 = 19 \]

### Step 5: Substitute back into the volume formula
Now substitute \( R^2 - r^2 \) back into the volume formula:

\[ \text{Volume} = \frac{22}{7} \times 25 \times 19 \]

### Step 6: Calculate the volume
Now calculate the volume:

\[ \text{Volume} = \frac{22}{7} \times 25 \times 19 \]

Calculating \( 25 \times 19 \):

\[ 25 \times 19 = 475 \]

Now substituting this back into the volume calculation:

\[ \text{Volume} = \frac{22}{7} \times 475 \]

Calculating \( \frac{22 \times 475}{7} \):

\[ 22 \times 475 = 10450 \]

Now divide by 7:

\[ \text{Volume} = \frac{10450}{7} \approx 1492.86 \, \text{cm}^3 \]

### Final Answer
Thus, the volume of the hollow cylinder is approximately:

\[ \text{Volume} \approx 1492.86 \, \text{cm}^3 \]