Respuesta :

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=100\pi \end{cases}\implies 100\pi =\pi r^2 \\\\\\ \cfrac{100\pi }{\pi }=r^2\implies 100=r^2\implies \sqrt{100}=r\implies \boxed{10=r}[/tex]

since a diameter is twice as long as the radius, this one is also 2r.
JeanaShupp

Answer: 20 units

Step-by-step explanation:

We know that the area of a circle is given by :-

[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.

We are given that the area of the circle = [tex]100\pi[/tex] square units.

[tex]\Rightarrow\ 100\pi=\pi r^2\\\\\Rightarrow\ r^2 =100[/tex]

Taking square root on both the sides , we get

[tex]\\\\\Rightarrow\ r=10[/tex]

The diameter of the circle is given by :-

[tex]d=2r=2(10)=20\text{ units}[/tex]

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