Given:
- Radius of the cylinder, [tex]\( r = 13 \, \text{m} \)[/tex]
- Volume of the cylinder, [tex]\( V = 19 \, \text{m}^3 \)[/tex]
We need to find the height of the cylinder, [tex]\( h \)[/tex], rounded to the nearest whole number. We use the formula for the volume of a cylinder:
[tex]\[ V = \pi r^2 h \][/tex]
Rearranging for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{V}{\pi r^2} \][/tex]
Substituting the given values into the formula:
[tex]\[ h = \frac{19}{\pi \times 13^2} \][/tex]
First, calculate [tex]\( 13^2 \)[/tex]:
[tex]\[ 13^2 = 169 \][/tex]
Now, we substitute this back into the equation:
[tex]\[ h = \frac{19}{\pi \times 169} \][/tex]
Let's break this down step by step:
1. Calculate [tex]\( \pi \times 169 \)[/tex]:
- The value of [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
- So, [tex]\( \pi \times 169 = 3.14159 \times 169 \approx 530.89441 \)[/tex]
2. Divide the volume by this result:
[tex]\[ h = \frac{19}{530.89441} \approx 0.03578631856504155 \][/tex]
The height [tex]\( h \)[/tex] of the cylinder, before rounding, is approximately 0.03578631856504155 meters.
Finally, we round this to the nearest whole number:
[tex]\[ h \approx 0 \][/tex]
So, the height of the cylinder, rounded to the nearest whole number, is 0 meters.
