The circumference of the base of a right circular cylinder is 44 cm and its height is 15 cm. The volume (in `cm^(3)`) of the cylinder is (use `pi=(22)/(7)`)

Options

A. 770
B. 1155
C. 1540
D. 2310

Answer

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

### Step 1: Understand the formula for the volume of a cylinder
The volume \( V \) of a right circular cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

### Step 2: Find the radius from the circumference
We know the circumference \( C \) of the base of the cylinder is 44 cm. The formula for the circumference of a circle is:
\[ C = 2\pi r \]
Substituting the given circumference:
\[ 44 = 2 \cdot \frac{22}{7} \cdot r \]

### Step 3: Solve for the radius \( r \)
Rearranging the equation to solve for \( r \):
\[ r = \frac{44 \cdot 7}{2 \cdot 22} \]
Calculating the right side:
\[ r = \frac{308}{44} = 7 \text{ cm} \]

### Step 4: Use the height of the cylinder
The height \( h \) of the cylinder is given as 15 cm.

### Step 5: Substitute \( r \) and \( h \) into the volume formula
Now we can substitute \( r \) and \( h \) into the volume formula:
\[ V = \pi r^2 h = \frac{22}{7} \cdot (7)^2 \cdot 15 \]

### Step 6: Calculate \( r^2 \)
Calculating \( r^2 \):
\[ r^2 = 7^2 = 49 \]

### Step 7: Substitute \( r^2 \) into the volume formula
Now substituting \( r^2 \) back into the volume formula:
\[ V = \frac{22}{7} \cdot 49 \cdot 15 \]

### Step 8: Simplify the volume calculation
Calculating the volume:
\[ V = 22 \cdot 7 \cdot 15 \]
\[ V = 1540 \text{ cm}^3 \]

### Final Answer
The volume of the cylinder is \( 1540 \text{ cm}^3 \).

---