Question

The area of the circle shown below is 100π. What is the diameter (D) of the circle?

Answer 1

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

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

Answer 2

Answer: 20 units

Step-by-step explanation:

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

$\text{Area}=\pi r^2$, where r is the radius of the circle.

We are given that the area of the circle = $100\pi$ square units.

$\Rightarrow\ 100\pi=\pi r^2\\\\\Rightarrow\ r^2 =100$

Taking square root on both the sides , we get

$\\\\\Rightarrow\ r=10$

The diameter of the circle is given by :-

$d=2r=2(10)=20\text{ units}$