Final answer:
To find the height of the cylinder, use the formula for the volume of a cylinder and the formula for the circumference of the base. Substitute the given values and solve for the height. The height of the cylinder is approximately 14.08 cm.
Step-by-step explanation:
To find the height of the cylinder, we can use the formula for the volume of a cylinder and the formula for the circumference of the base.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
The circumference of the base is given by the formula C = 2πr, where r is the radius.
From the given information, we know that the volume of the cylinder is 539 cm³ and the circumference of the base is 22 cm.
Let's solve for the height:
- First, let's find the radius using the formula for circumference:
- C = 2πr
- 22 cm = 2πr
- r = 22 / (2π) ≈ 3.5 cm
Now, let's substitute the radius into the formula for volume:
- 539 cm³ = π(3.5 cm)²h
- 539 cm³ = 12.25πh
- h = 539 cm³ / 12.25π ≈ 14.08 cm
Therefore, the height of the cylinder is approximately 14.08 cm.