NEED HELP WITH GEOMETRY HOMEWORK!!! PLEASE PLEASE HELP!!

Question

A circle has a radius of 5 cm. If the area is tripled, what happens to the circumference?

Please give the explanation and the answer.

Answer 1

A circle has a radius of 5 cm. If the area is tripled, what happens to the circumference?

Please give the explanation and the answer.

The circumference of a circle with a radius r is C = 2⋅π⋅r

The circumference of a circle with a radius 5 is C = 10π

The area of a circle with radius r is A = π⋅r²

The area of a circle with radius 5 is A = 25π

Tripling the area of the circle, A = 3 •25π = 75π

To determine how this affects the circumference,

1.  solve the equation A = π⋅r2 for r. r = square root of (Area / π)
2.  plug r into the circumference formula. A circle with A = 75π has radius r = square root (75) and circumference C = 2 • square root (75) • π

Relationship: (radicals are not simplified intentionally)

A circle with A = 25π has radius r = square root (25) and circumference C = 2 • square root (25) • π

A circle with A = 75π has radius r = square root (75) and circumference C = 2 • square root (75) • π 

Answer 2

Hi Becky,

You know area of circle = Π r²

you have r = 5 so area = 25 Π is it correct? and circumstance = 2 Π *5 = 10Π

Now, area times 3 it means 25Π *3 = 75 Π is new area you need to know what effects on circumstance

In fact, when area is 75Π you need to find new radius so 75Π = ΠR² both side divided by Π

75 = R²

25 * 5 - R²

5√5 = R

and circumstance = 2 * 5√5Π = 10√5 Π

As a result, when radius is 5, area times 3, circumstance will be √5 time priority of circumstance

I hope it is useful and let me know if you have any question.

Minoo