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 √(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

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}`