Question

find the diameter of the circle whose area is 2200/7 square cm.

Answer 1

area of circle = πr²

2200/7 = 22/7 * r²

100 = 7 * 7 * r²

r² = 100/49

r = √100/49

r = 10/7

diameter of circle = 2 * 10/7

= 20/7cm

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Answer 2

Diameter of given circle = 20 cm

Step-by-step explanation:

Given: Area of a circle = $\frac{2200}{7}$ square cm.

And, we also have the formula for area of a circle.

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

So, lets equate both the areas and then solve for 'r'.

Equating both, we get,

$\pi r^{2} = \frac{2200}{7}\\\\\Rightarrow \frac{22}{7} \times r^{2} = \frac{2200}{7}\\\\\\\Rightarrow r^{2} = \frac{2200}{7} \times \frac{7}{22}\\\\\Rightarrow r^{2} = 100\\\\\Rightarrow r = \sqrt{100}\\\\\Rightarrow r = \pm 10$

but we will neglect (-10) as radius can only be positive.

So, r = 10 cm

Now, we have to find the diameter.

since, $Diameter \ = \ 2 \times Radius = 2 \times 10 = 20 \ cm$

So, Diameter = 20 cm.