Circumference: Using variables

The area of the rectangle in the drawing is 28X cm².

What is the area of the circle?

Let's draw the center of the circle and we can divide the diameter of the circle into two equal radii

Now let's calculate the length of the radii as follows:

$7\times2r=28x$

$14r=28x$

We'll divide both sides by 14:

$r=\frac{28}{14}x$

$r=2x$

Let's calculate the circumference of the circle:

$P=2\pi\times r=2\pi\times2x=4\pi x$

$4\pi x$

What is the radius of a circle that has a circumference of $9a\pi$ cm?

$4.5a$ cm

A circle has a circumference measuring $4x\pi$ cm.

How will the circumference change if we increase the radius of the circle by 2 cm?

It will increase by $4\pi$ cm.

A circle has an area of $81a^2\pi$.

What is its circumference?

$18a\pi$ cm

The circumference of the circle in the diagram is $36a^2$ cm.

BO is the radius.

ABCD is a parallelogram.
BO is perpendicular to DC.

DC = $\frac{4}{a}$

What is the area of the parallelogram?

$72\frac{a}{\pi}$ cm²