The volume of a right circular cylinder whose height is 40cm, and circumference of its base is 66 cm, is:

Options

A. `55440 cm^3`
B. `3465 cm^3`
C. ` 7720 cm^3`
D. `13860 cm^3`

Answer

To find the volume of a right circular cylinder, we can use the formula:

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

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

Given:
- Height \( h = 40 \) cm,
- Circumference of the base \( C = 66 \) cm.

### Step 1: Find the radius of the base

The circumference of a circle is given by the formula:

\[ C = 2 \pi r \]

We can rearrange this formula to solve for the radius \( r \):

\[ r = \frac{C}{2 \pi} \]

Substituting the given circumference:

\[ r = \frac{66}{2 \pi} \]

Using \( \pi \approx \frac{22}{7} \):

\[ r = \frac{66}{2 \times \frac{22}{7}} \]

Calculating the denominator:

\[ 2 \times \frac{22}{7} = \frac{44}{7} \]

Now substituting back to find \( r \):

\[ r = \frac{66 \times 7}{44} \]

Calculating \( r \):

\[ r = \frac{462}{44} = 10.5 \text{ cm} \]

### Step 2: Calculate the volume

Now that we have the radius, we can substitute \( r \) and \( h \) into the volume formula:

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

Substituting the values:

\[ V = \pi (10.5)^2 (40) \]

Calculating \( (10.5)^2 \):

\[ (10.5)^2 = 110.25 \]

Now substituting this back into the volume formula:

\[ V = \pi \times 110.25 \times 40 \]

Using \( \pi \approx \frac{22}{7} \):

\[ V = \frac{22}{7} \times 110.25 \times 40 \]

Calculating \( 110.25 \times 40 \):

\[ 110.25 \times 40 = 4410 \]

Now substituting this back:

\[ V = \frac{22}{7} \times 4410 \]

Calculating \( \frac{22 \times 4410}{7} \):

\[ 22 \times 4410 = 97020 \]

Now dividing by 7:

\[ V = \frac{97020}{7} = 13860 \text{ cm}^3 \]

### Final Answer

The volume of the right circular cylinder is:

\[ \boxed{13860 \text{ cm}^3} \]

---