Question

consider the following when r = 8 cm. give both exact values and approximations to the nearest hundredth. (a) find the circumference of the figure. cm ≈ cm (b) find the area of the figure. cm² ≈ cm²

Explanation:

Step1: Recall Circumference Formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \). Given \( r = 8 \) cm.
Substitute \( r = 8 \) into the formula: \( C = 2\pi(8)=16\pi \) cm (exact value).
For approximation, use \( \pi \approx 3.14159 \): \( 16\times3.14159\approx50.27 \) cm.

Step2: Recall Area Formula

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Given \( r = 8 \) cm.
Substitute \( r = 8 \) into the formula: \( A=\pi(8)^{2}=64\pi \) \( \text{cm}^2 \) (exact value).
For approximation, use \( \pi \approx 3.14159 \): \( 64\times3.14159\approx201.06 \) \( \text{cm}^2 \).

Answer:

(a) Exact: \( 16\pi \) cm, Approximation: \( 50.27 \) cm
(b) Exact: \( 64\pi \) \( \text{cm}^2 \), Approximation: \( 201.06 \) \( \text{cm}^2 \)