Question

invent a story of how jada fills the aquarium that fits the graph
3 from unit 5, lesson 4
recall the formula for area of a circle.
a. write an equation relating a circle’s radius, r, and area, a.
b. is area a function of the radius? is radius a function of the area?
c. fill in the missing parts of the table.

r	3		\\(\frac{1}{2}\\)
a		16π		100π

Explanation:

Step1: For \( r = 3 \)

Use the formula \( A=\pi r^{2} \). Substitute \( r = 3 \) into the formula: \( A=\pi\times3^{2}=9\pi \).

Step2: For \( A = 16\pi \)

We know \( A=\pi r^{2} \), so \( 16\pi=\pi r^{2} \). Divide both sides by \( \pi \): \( 16 = r^{2} \). Take the square root: \( r = 4 \) (since radius is positive).

Step3: For \( r=\frac{1}{2} \)

Substitute \( r=\frac{1}{2} \) into \( A=\pi r^{2} \): \( A=\pi\times(\frac{1}{2})^{2}=\frac{\pi}{4} \).

Step4: For \( A = 100\pi \)

Use \( A=\pi r^{2} \), so \( 100\pi=\pi r^{2} \). Divide by \( \pi \): \( 100 = r^{2} \). Take the square root: \( r = 10 \) (positive radius).

Answer:

\( r \)	3	4	\( \frac{1}{2} \)	10