Final answer:
Using the formula for the volume of a cylinder, V = πr²h, and plugging in the given volume and radius (2²), you can solve for the height, resulting in a height of 1.375 for the cylinder.
Step-by-step explanation:
To calculate the height of a cylinder when you know the volume and the radius, you use the volume formula for a cylinder, which is V = πr²h. In this given problem, the volume (V) is 22π (where π is Pi, approximately 3.14159), and the radius (r) is provided as 2², which is 4 when squared. Inserting these values into the formula gives us 22π = π·4²h. This simplifies to 22π = 16πh. When you divide both sides of the equation by 16π, you are left with h = 22/16, which reduces to h = 1.375.
This calculation relies on understanding the relationship between the volume of a cylinder and its dimensions as well as basic algebra to solve for the unknown variable, which in this case is the cylinder's height (h).
To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is V = πr²h. In this case, the radius is 2^2, which is 4, and the volume is given as 22π. We can substitute these values into the formula and solve for h.
V = πr²h
22π = π(4)²h
22π = 16πh
Divide both sides of the equation by 16π:
22 = 16h
Divide both sides by 16:
h = 22/16
Simplifying the fraction:
h = 11/8
So, the height of the cylinder is 11/8 or 1.375 units.