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

C = 2*π*r

3π = 2π*r

$\frac{3\pi }{2\pi } = \frac{2\pi *r}{2\pi }$

$\frac{3}{2} = r$

A = π * r²

   = π $(\frac{3}{2} )^{2}$

   = π $(\frac{9}{4} )$

Answer: C