Question

if the circumference of a circle measures 3π cm, what is the area of the circle in terms of π? A) 3 4 π cm2 b) 3 2 π cm2 c) 9 4 π cm2 d) 9 2 π cm2

Answer 1

The circumference of a circle is given by

$C = 2\pi r$

Where r is the radius of the circle. So, you have

$3\pi = 2\pi r \iff 2r = 3 \iff r = \dfrac{3}{2}$

The area of a circle is given by

$A = 2\pi r^2$

If you plug the value for r you have

$A = 2 \pi \left(\dfrac{3}{2}\right)^2 = 2\pi\dfrac{9}{4} = \dfrac{9}{2}\pi$

Answer 2

The circumference of a circle measures 3π cm, and the area of the circle in terms of π is 9π/4.

What is the circumference of a circle?

The Circumference (or) perimeter of the circle = 2πR.

Where R is the radius of the circle.

The circumference of a circle measures 3π cm.

The area of the circle is given by;

$\rm Area =\pi r^2$

The circumference of the circle is;

$\rm Circumference = 2\pi r\\\\3\pi =2\pi r\\\\r =\dfrac{3\pi }{2\pi }\\\\r=\dfrac{3}{2}$

The area of the circle is;

$\rm Area =\pi r^2\\\\Area =\pi \times \left( \dfrac{3}{2} \right )^2\\\\Area =\dfrac{9\pi }{4}$

Hence, the area of the circle in terms of π is 9π/4.

Learn more about the area of the circle here;

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