The problem asks to approximate the circumference $C$ and area $A$ of a circle with radius $r = 1 \, \text{cm}$, using $\pi \approx \frac{22}{7}$.

1. Circumference:

The formula for the circumference of a circle is: $C = 2 \pi r$ Substitute $\pi \approx \frac{22}{7}$ and $r = 1 \, \text{cm}$: $C \approx 2 \times \frac{22}{7} \times 1 = \frac{44}{7} \, \text{cm}$ So, the circumference $C \approx \frac{44}{7} \, \text{cm}$.

2. Area:

The formula for the area of a circle is: $A = \pi r^2$ Substitute $\pi \approx \frac{22}{7}$ and $r = 1 \, \text{cm}$: $A \approx \frac{22}{7} \times 1^2 = \frac{22}{7} \, \text{cm}^2$ So, the area $A \approx \frac{22}{7} \, \text{cm}^2$.

Final answers:

• $C \approx \frac{44}{7} \, \text{cm}$
• $A \approx \frac{22}{7} \, \text{cm}^2$

Let me know if you want any further clarification or details.

Here are 5 related questions:

1. How would the circumference and area change if the radius was doubled?
2. What would the exact circumference be if $\pi$ was used instead of $\frac{22}{7}$?
3. How does the approximation of $\frac{22}{7}$ for $\pi$ affect the precision of the area and circumference?
4. Can the radius be a fraction? If so, how would the formulas be adjusted?
5. What is the relationship between the diameter and the circumference of a circle?

Tip: Always keep track of units, especially when dealing with area and circumference.