What is the diameter in centimeters of a circle whose area is $100\pi \text{cm}^2$?
The area is $100\pi=\pi r^2$, so $r=10$. The diameter is $2r=\boxed{20}$ centimeters.
20
Level 3
Prealgebra
Problem: What is the diameter in centimeters of a circle whose area is $100\pi \text{cm}^2$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the diameter of the circle, we first need to use the formula for the area of a circle, which is given by \( A = \pi r^2 \), where \( r \) is the radius. We know the area is \( 100\pi \text{cm}^2 \). 

Setting the area formula equal to the given area, we have:

\[
\pi r^2 = 100\pi
\]

Next, we can simplify this equation by dividing both sides by \( \pi \):

\[
r^2 = 100
\]

To solve for \( r \), we take the square root of both sides:

\[
r = \sqrt{100} = 10 \text{ cm}
\]

Now that we have the radius, we need to find the diameter. The diameter \( d \) of a circle is twice the radius:

\[
d = 2r
\]

Substituting the value of \( r \):

\[
d = 2 \times 10 \text{ cm} = 20 \text{ cm}
\]

Thus, the final answer is \( 20 \).<|END_OF_LATENT|> The final answer is $20$.