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

Options

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

Answer

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

### Step 1: Identify the given values
- The diameter of the base of the cylinder is 14 cm.
- The height of the cylinder is 80 cm.

### Step 2: Calculate the radius
The radius (r) is half of the diameter.
\[ r = \frac{\text{diameter}}{2} = \frac{14 \text{ cm}}{2} = 7 \text{ cm} \]

### Step 3: Use the volume formula for a cylinder
The formula for the volume (V) of a cylinder is given by:
\[ V = \pi r^2 h \]
Where:
- \( \pi \) is approximately \( \frac{22}{7} \) (or you can use 3.14 for more precision)
- \( r \) is the radius
- \( h \) is the height

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ V = \frac{22}{7} \times (7 \text{ cm})^2 \times 80 \text{ cm} \]

### Step 5: Calculate \( r^2 \)
\[ (7 \text{ cm})^2 = 49 \text{ cm}^2 \]

### Step 6: 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
First, calculate \( \frac{22}{7} \times 49 \):
\[ \frac{22 \times 49}{7} = 22 \times 7 = 154 \]
Now substitute this back into the volume formula:
\[ V = 154 \times 80 \text{ cm}^3 \]

### Step 8: Calculate the final volume
\[ V = 12320 \text{ cm}^3 \]

### Conclusion
The volume of the cylinder is \( 12320 \text{ cm}^3 \).

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