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A circle has a diameter of 10 centimeters. The area of that circle is then increased to nine times the original size. What will the new diameter be?

Respuesta :

First, you would find the area f the circle you have now. The equation for that would be πr^2. So you would find the radius, half the diameter, which is 5. 5 squared is 25 and multiplying that by 3.14, pi, you would get 78.5. You would then multiply 78.5 by 9 getting 706.5. To get the diameter of this circle you would start by dividing 706.5 by 3.14. That answer would be 225. You would then find the square root of 225, which would be 15. Finally, you would multiply 15 times two to get the diameter.
Hello, let's find the area of the circle.

First of all, we need the radius, that is half the diameter so r = d/2

r = 10/2 = 5 cm

Then A = πr² = 5²π = 25π cm²

So, the new area is 9 times the original one, so A*9

New area = 25π * 9 = 225π cm²

Let's find the new diameter [tex] \sqrt \frac{4A}{ \pi } [/tex] = [tex] \sqrt \frac{4*225 \pi }{ \pi } [/tex]

d = √900 = 30 cm