To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by:
Volume = π * r^2 * h
Where:
- Volume is the given volume of the cylinder (2000 cm³)
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder (half of the diameter, which is 12 cm / 2 = 6 cm)
- h is the height of the cylinder (what we're trying to find)
Let's substitute the values into the formula and solve for h:
2000 = π * (6^2) * h
Simplifying further:
2000 = π * 36 * h
To solve for h, we can rearrange the equation:
h = 2000 / (π * 36)
Now, we can calculate the height of the cylinder:
h = 2000 / (3.14159 * 36)
h ≈ 17.75 cm
Therefore, the height of the cylinder is approximately 17.75 cm.