A cylinder with diameter of base 14 cm and height 80 cm. The volume of this cylinder would be

Options

A. `11780cm^(3)`
B. `11940cm^(3)`
C. `12280cm^(3)`
D. `12320cm^(3)`

Answer

To find the volume of a cylinder, we can follow these steps:

### Step 1: Identify the given values
- **Diameter of the base (d)** = 14 cm
- **Height (h)** = 80 cm

### Step 2: Calculate the radius
The radius (r) is half of the diameter.

\[ r = \frac{d}{2} = \frac{14 \text{ cm}}{2} = 7 \text{ cm} \]

### Step 3: Use the formula for the volume of a cylinder
The formula for the volume (V) of a cylinder is given by:

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

### Step 4: Substitute the values into the formula
Using \(\pi \approx \frac{22}{7}\), we can substitute the values of r and h into the formula:

\[ V = \frac{22}{7} \times (7 \text{ cm})^2 \times 80 \text{ cm} \]

### Step 5: Calculate \(r^2\)
First, calculate \(r^2\):

\[ r^2 = 7^2 = 49 \text{ cm}^2 \]

### Step 6: Substitute \(r^2\) back into the volume formula
Now substitute \(r^2\) back into the volume formula:

\[ V = \frac{22}{7} \times 49 \text{ cm}^2 \times 80 \text{ cm} \]

### Step 7: Simplify the equation
Now, we can simplify the equation. The \(7\) in the denominator cancels with one of the \(7\)s in \(49\):

\[ V = 22 \times 7 \times 80 \]

### Step 8: Calculate the final volume
Now, perform the multiplication:

\[ V = 22 \times 7 = 154 \]
\[ V = 154 \times 80 = 12320 \text{ cm}^3 \]

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

\[ V = 12320 \text{ cm}^3 \]