Let's analyze the table you uploaded and solve the problem step by step.

The table contains four columns: Radius, Diameter, Area, and Circumference. The relations between these values for a circle are given by the following formulas:

1. Diameter: $D = 2R$ (where $R$ is the radius)
2. Circumference: $C = 2\pi R$
3. Area: $A = \pi R^2$

Now, let's fill in the missing values using these relationships.

First Row

• Radius = 2
  • Diameter: $D = 2 \times 2 = 4$
  • Circumference: Already given as $4\pi$, which matches $2\pi \times 2$.
  • Area: $A = \pi \times 2^2 = 4\pi$

Second Row

• Radius = 4
  • Diameter: $D = 2 \times 4 = 8$
  • Circumference: Already given as $8\pi$, which matches $2\pi \times 4$.
  • Area: $A = \pi \times 4^2 = 16\pi$

Third Row

• Radius = 6
  • Diameter: Already given as 12
  • Circumference: Already given as $12\pi$, which matches $2\pi \times 6$.
  • Area: $A = \pi \times 6^2 = 36\pi$

Fourth Row

• Radius = 8
  • Diameter: Already given as 16
  • Circumference: Missing, so $C = 2\pi \times 8 = 16\pi$
  • Area: Already given as $64\pi$, which matches $\pi \times 8^2$.

Fifth Row

• Radius = 10
  • Diameter: Already given as 20
  • Circumference: $C = 2\pi \times 10 = 20\pi$
  • Area: $A = \pi \times 10^2 = 100\pi$

Completed Table:

Would you like further clarification on any of these values?

Here are some related questions for practice:

1. How does the circumference change if the radius is doubled?
2. What is the relationship between area and radius?
3. Can you derive the diameter if you only know the circumference?
4. What happens to the area if the radius increases by 50%?
5. How does the area change if the circumference is doubled?

Tip: The area of a circle grows quadratically with respect to the radius, while the circumference grows linearly.