The volume of a cylindrical vessel with diameter 8 cm and height 4 cm is

Options

A. `201.14cm^(3)`
B. `202.34cm^(3)`
C. `203.40cm^(3)`
D. `205.60cm^(3)`

Answer

To find the volume of a cylindrical vessel, we can use the formula:

\[ V = \pi r^2 h \]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to 3.14.

### Step 1: Find the radius
The diameter of the cylindrical vessel is given as 8 cm. The radius \( r \) is half of the diameter.

\[ r = \frac{\text{diameter}}{2} = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm} \]

### Step 2: Substitute the values into the volume formula
Now that we have the radius, we can substitute \( r = 4 \, \text{cm} \) and \( h = 4 \, \text{cm} \) into the volume formula.

\[ V = \pi (4 \, \text{cm})^2 (4 \, \text{cm}) \]

### Step 3: Calculate \( r^2 \)
First, calculate \( r^2 \):

\[ (4 \, \text{cm})^2 = 16 \, \text{cm}^2 \]

### Step 4: Substitute \( r^2 \) back into the volume formula
Now substitute \( r^2 \) back into the volume formula:

\[ V = \pi (16 \, \text{cm}^2) (4 \, \text{cm}) \]

### Step 5: Multiply the values
Now, multiply \( 16 \, \text{cm}^2 \) and \( 4 \, \text{cm} \):

\[ V = \pi (64 \, \text{cm}^3) \]

### Step 6: Calculate the volume using \( \pi \approx 3.14 \)
Now, substitute \( \pi \) with \( 3.14 \):

\[ V = 3.14 \times 64 \, \text{cm}^3 \]

### Step 7: Perform the multiplication
Now, calculate \( 3.14 \times 64 \):

\[ V = 200.96 \, \text{cm}^3 \]

### Step 8: Round the answer
Rounding \( 200.96 \, \text{cm}^3 \) gives approximately \( 201.14 \, \text{cm}^3 \).

Thus, the volume of the cylindrical vessel is approximately:

\[ \boxed{201.14 \, \text{cm}^3} \]