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To solve this, let’s use the provided radius \( r = 7 \) cm to find the circumference and area of the circle. Here’s the step-by-step solution:

### (a) Find the circumference of the circle
The formula for the circumference \( C \) of a circle is:
\[
C = 2 \pi r
\]

Substitute \( r = 7 \) cm:
\[
C = 2 \pi \times 7 = 14 \pi \text{ cm}
\]

For the approximate value, use \( \pi \approx 3.14 \):
\[
C \approx 14 \times 3.14 = 43.96 \text{ cm}
\]

**Exact Circumference**: \( 14 \pi \) cm  
**Approximate Circumference**: \( 43.96 \) cm

### (b) Find the area of the circle
The formula for the area \( A \) of a circle is:
\[
A = \pi r^2
\]

Substitute \( r = 7 \) cm:
\[
A = \pi \times 7^2 = \pi \times 49 = 49 \pi \text{ cm}^2
\]

For the approximate value:
\[
A \approx 49 \times 3.14 = 153.86 \text{ cm}^2
\]

**Exact Area**: \( 49 \pi \) cm²  
**Approximate Area**: \( 153.86 \) cm²

Let me know if you'd like more details on any part of the solution, or have questions!

### Related Questions
1. What would the circumference and area be if the radius were doubled?
2. How does changing the radius affect the area compared to the circumference?
3. What is the diameter of the circle, and how does it relate to the radius?
4. How would the results change if \( \pi \) were approximated as 3.14159 instead?
5. Can we express the circumference and area formulas in terms of the diameter instead of the radius?

### Tip:
Using \( \pi \approx 3.14 \) is a common approximation, but for more precision, \( \pi \approx 3.14159 \) can be used to get closer to the exact value.

Consider the following when r = 7 cm. Give both exact values and approximations to the nearest hundredth. (a) Find the circumference of the figure. (b) Find the area of the figure.

Learn how to calculate the exact and approximate circumference and area of a circle with a radius of 7 cm. This geometry problem includes detailed explanations using the circumference and area formulas for circles, with step-by-step solutions for both exact and approximate values.

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