Question

fill in the correct formula for each measurement. area of a circle: a = circumference of a circle (given diameter): c = constant of proportionality: k = proportional relationship: y = circumference of a circle (given r): c =

Explanation:

Step1: Recall area formula

The area of a circle with radius $r$ is $A = \pi r^{2}$.

Step2: Recall circumference - diameter formula

The circumference of a circle with diameter $d$ is $C=\pi d$.

Step3: Recall constant of proportionality

In a proportional relationship $y = kx$, the constant of proportionality $k$ is a non - zero real number. In the context of a circle's circumference $C$ and diameter $d$ ($C=\pi d$), $k = \pi$. In a general proportional relationship $y=kx$.

Step4: Recall proportional relationship formula

The general form of a proportional relationship is $y = kx$, where $k$ is the constant of proportionality.

Step5: Recall circumference - radius formula

The circumference of a circle with radius $r$ is $C = 2\pi r$.

Answer:

Area of a circle: $A=\pi r^{2}$
Circumference of a circle (given diameter): $C = \pi d$
Constant of proportionality: $k=\pi$ (in circle - related context, in general $k$ is non - zero real number in $y = kx$)
Proportional relationship: $y = kx$
Circumference of a circle (given $r$): $C = 2\pi r$