To solve for the radius of a cylinder with a height that is twice its radius and a lateral area of 16π square units, we can start by recalling the formula for the lateral area of a cylinder:
Lateral Area = 2πrh
In this formula:
- r is the radius of the cylinder
- h is the height of the cylinder
Given that the height h is twice the radius, we can express this relationship mathematically as:
h = 2r
Now, we can substitute this expression for h into the lateral area formula:
Lateral Area = 2πr(2r)
This simplifies to:
Lateral Area = 4πr2
We know from the problem statement that the lateral area is 16π. Therefore, we can set the two expressions for lateral area equal to each other:
4πr2 = 16π
Next, we can divide both sides of the equation by 4π:
r2 = 16/4
This simplifies down to:
r2 = 4
To find the radius r, we take the square root of both sides:
r = √4
Therefore:
r = 2
In conclusion, the radius of the cylinder is 2 units.