The circumference of the circular base of a cylinder is 44 cm and its height is 15 cm. The volume of the cylinder is

Options

A. `1155cm^(3)`
B. `2310cm^(3)`
C. `770cm^(3)`
D. `1540 cm^(3)`

Answer

To find the volume of the cylinder given its circumference and height, we can follow these steps:

### Step 1: Understand the given information
We know the circumference (C) of the circular base of the cylinder is 44 cm, and the height (h) of the cylinder is 15 cm.

### Step 2: Use the formula for circumference
The formula for the circumference of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circular base.

### Step 3: Solve for the radius (r)
We can rearrange the formula to find the radius:
\[ r = \frac{C}{2\pi} \]
Substituting the given value of \( C \):
\[ r = \frac{44}{2\pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{44}{2 \times \frac{22}{7}} \]
\[ r = \frac{44 \times 7}{2 \times 22} \]
\[ r = \frac{308}{44} \]
\[ r = 7 \text{ cm} \]

### Step 4: Use the volume formula for a cylinder
The formula for the volume (V) of a cylinder is:
\[ V = \pi r^2 h \]
Substituting the values of \( r \) and \( h \):
\[ V = \pi \times (7)^2 \times 15 \]
\[ V = \pi \times 49 \times 15 \]

### Step 5: Substitute the value of π
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 49 \times 15 \]

### Step 6: Simplify the expression
Calculating \( 49 \times 15 \):
\[ 49 \times 15 = 735 \]
Now substituting back:
\[ V = \frac{22}{7} \times 735 \]
To simplify:
\[ V = 22 \times 105 \]
\[ V = 2310 \text{ cm}^3 \]

### Final Answer
The volume of the cylinder is \( 2310 \text{ cm}^3 \).

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