Cylinder Volume Calculation

This problem requires calculating the volume of a cylinder using its given radius and height.

Given Data:

• Radius ($r$) = 38.5 cm
• Height ($h$) = 18 cm
• Value of $\pi$ = 22/7

Volume Formula and Application

The formula for the volume ($V$) of a cylinder is:

$V = \pi r^2 h$

First, convert the radius from decimal to a fraction:

$r = 38.5 = \frac{385}{10} = \frac{77}{2}$ cm

Substitute the values into the volume formula:

$V = \frac{22}{7} \times \left(\frac{77}{2}\right)^2 \times 18$

Calculation Steps

1. Expand the square of the radius:

   $V = \frac{22}{7} \times \frac{77}{2} \times \frac{77}{2} \times 18$

2. Combine terms and simplify:

   $V = \frac{22 \times 77 \times 77 \times 18}{7 \times 2 \times 2}$

3. Cancel out the factor of 7 from 77 in the numerator and 7 in the denominator:

   $V = \frac{22 \times (7 \times 11) \times 77 \times 18}{7 \times 4}$

   $V = \frac{22 \times 11 \times 77 \times 18}{4}$

4. Simplify further by dividing 22 by 2 and 4 by 2:

   $V = \frac{11 \times 11 \times 77 \times 18}{2}$

5. Divide 18 by 2:

   $V = 11 \times 11 \times 77 \times 9$

6. Perform the multiplication:

   $V = 121 \times 77 \times 9$

   $V = 9317 \times 9$

   $V = 83853$

Result

The volume of the cylinder is $83853$ $cm^3$.