What is the area of the gray region, in square units, if the radius of the larger circle is four times the radius of the smaller circle and the diameter of the smaller circle is 2 units? Express your answer in terms of $\pi$. [asy]
size(150);
pair A, B;
A=(0,0);
B=(-4,1);
fill(circle(A, 8), gray(.7));
fill(circle(B, 2), white);
draw(circle(A, 8));
draw(circle(B, 2));
[/asy]
If the diameter of the small circle is 2, then the radius is 1. Thus, the radius of the large circle is 4 times this, or 4. The area of the large circle is then $\pi4^2=16\pi$ and the area of the small circle is $\pi 1^2=1\pi$. We can then find the gray area to be the difference in these, or $16\pi-1\pi=\boxed{15\pi} \text{sq units}$.
15\pi
Level 4
Prealgebra
Problem: What is the area of the gray region, in square units, if the radius of the larger circle is four times the radius of the smaller circle and the diameter of the smaller circle is 2 units? Express your answer in terms of $\pi$. [asy]
size(150);
pair A, B;
A=(0,0);
B=(-4,1);
fill(circle(A, 8), gray(.7));
fill(circle(B, 2), white);
draw(circle(A, 8));
draw(circle(B, 2));
[/asy]
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the area of the gray region, first determine the radius of the smaller circle. The diameter of the smaller circle is given as 2 units, so the radius is half of the diameter: 

Radius of smaller circle = 2 units / 2 = 1 unit.

Next, calculate the radius of the larger circle. The problem states that the radius of the larger circle is four times the radius of the smaller circle:

Radius of larger circle = 4 * Radius of smaller circle = 4 * 1 unit = 4 units.

Now, calculate the area of both circles. The area of a circle is given by the formula A = πr², where r is the radius.

Area of the larger circle:
A_larger = π * (4 units)² = π * 16 = 16π square units.

Area of the smaller circle:
A_smaller = π * (1 unit)² = π * 1 = π square unit.

To find the area of the gray region, subtract the area of the smaller circle from the area of the larger circle:

Area of gray region = Area of larger circle - Area of smaller circle = 16π - π = 15π square units.

Thus, the final answer is 15π.<|END_OF_LATENT|> The final answer is $15\pi$.