To find the height of a cylinder when you know the volume and the radius, you can use the following formula:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume of the cylinder.
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
- \( \pi \) is a constant that approximately equals 3.14159.
Given:
- The volume (\( V \)) of the cylinder is 35 cubic centimeters.
- The radius (\( r \)) of the base of the cylinder is 12 centimeters.
You want to solve for \( h \), the height of the cylinder. Rearrange the formula to isolate \( h \):
\[ h = \frac{V}{\pi r^2} \]
Now plug in the values:
\[ h = \frac{35}{\pi (12)^2} \]
\[ h = \frac{35}{3.14159 \times 144} \]
\[ h = \frac{35}{3.14159 \times 144} \]
\[ h = \frac{35}{452.38896} \]
\[ h \approx 0.0774 \text{ centimeters} \]
Therefore, the height of the cylinder is approximately 0.0774 centimeters.
