A circular spinner for a game has a radius of 5 cm. The probability of winning on one spin of this spinner is $\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\pi$.

[asy]import graph;
draw(Circle((0,0),25),black);
draw((0,0)--(7,18),Arrow);
draw((0,0)--(0,25));
draw((0,0)--(15,-20));
label("WIN",(10,10),S);
label("LOSE",(-8,-8),N);
dot((0,0));
[/asy]
The probability of winning on one spin is equal to the ratio of the area of the WIN sector to the area of the entire circle. The area of the entire circle is $\pi \cdot 5^2 = 25\pi$. In math terms, our ratio is: $\frac{2}{5}=\frac{\text{area of the win sector}}{25\pi}$. Solving for the area of the win sector, we find it equal to $\boxed{10\pi}$ square centimeters.
10\pi
Level 2
Geometry
Problem: A circular spinner for a game has a radius of 5 cm. The probability of winning on one spin of this spinner is $\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\pi$.

[asy]import graph;
draw(Circle((0,0),25),black);
draw((0,0)--(7,18),Arrow);
draw((0,0)--(0,25));
draw((0,0)--(15,-20));
label("WIN",(10,10),S);
label("LOSE",(-8,-8),N);
dot((0,0));
[/asy]
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the area of the WIN sector, we first need to calculate the total area of the circular spinner. The formula for the area of a circle is A = πr², where r is the radius. Given that the radius is 5 cm, we substitute this value into the formula: 

A = π(5 cm)² = π(25 cm²) = 25π cm².

Next, we know that the probability of winning on one spin of the spinner is given as 2/5. This probability represents the fraction of the total area that corresponds to the WIN sector. To find the area of the WIN sector, we multiply the total area of the circle by the probability of winning:

Area of WIN sector = (Probability of WIN) × (Total Area) = (2/5) × (25π cm²).

Now, we perform the multiplication:

Area of WIN sector = (2/5) × 25π cm² = (2 × 25/5)π cm² = (50/5)π cm² = 10π cm².

Thus, the area of the WIN sector is 10π cm².<|END_OF_LATENT|> The final answer is $10\pi$.