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. 2310
B. 770
C. 1155
D. 1540

Answer

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

### Step 1: Use the formula for the circumference of a circle
The circumference \( C \) of the base of the cylinder is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the base.

### Step 2: Substitute the given circumference
We know that the circumference \( C \) is 44 cm. Thus, we can set up the equation:
\[ 44 = 2 \pi r \]

### Step 3: Substitute the value of \( \pi \)
Using the value of \( \pi = \frac{22}{7} \), we can substitute this into the equation:
\[ 44 = 2 \times \frac{22}{7} \times r \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 44 = \frac{44}{7} r \]

### Step 5: Solve for \( r \)
To isolate \( r \), multiply both sides by \( 7 \):
\[ 44 \times 7 = 44r \]
\[ 308 = 44r \]
Now, divide both sides by 44:
\[ r = \frac{308}{44} = 7 \text{ cm} \]

### Step 6: Use the formula for the volume of a cylinder
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( h \) is the height of the cylinder.

### Step 7: Substitute the values of \( r \) and \( h \)
We have \( r = 7 \) cm and \( h = 15 \) cm. Substituting these values into the volume formula:
\[ V = \frac{22}{7} \times (7)^2 \times 15 \]

### Step 8: Calculate \( r^2 \)
Calculate \( r^2 \):
\[ (7)^2 = 49 \]

### Step 9: Substitute \( r^2 \) back into the volume formula
Now substitute \( 49 \) back into the volume formula:
\[ V = \frac{22}{7} \times 49 \times 15 \]

### Step 10: Simplify the volume calculation
First, simplify \( \frac{22}{7} \times 49 \):
\[ \frac{22 \times 49}{7} = 22 \times 7 = 154 \]
Now, multiply by the height:
\[ V = 154 \times 15 \]

### Step 11: Calculate the final volume
Now calculate \( 154 \times 15 \):
\[ V = 2310 \text{ cm}^3 \]

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

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