Question

geometry
circumference and area of a circle
find the circumference and the area of a circle with radius 3 yd.
use the value 3.14 for π, and do not round your answers. be sure to include the correct units in your answers.
3 yd
circumference:
area:
yd yd² yd³

Explanation:

Step1: Recall Circumference Formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius. Here, \( r = 3 \) yd and \( \pi = 3.14 \). Substitute the values: \( C = 2 \times 3.14 \times 3 \).

Step2: Calculate Circumference

\( 2 \times 3.14 = 6.28 \), then \( 6.28 \times 3 = 18.84 \). So circumference is \( 18.84 \) yd.

Step3: Recall Area Formula

The formula for the area \( A \) of a circle is \( A = \pi r^2 \). Substitute \( r = 3 \) yd and \( \pi = 3.14 \): \( A = 3.14 \times 3^2 \).

Step4: Calculate Area

First, \( 3^2 = 9 \), then \( 3.14 \times 9 = 28.26 \). So area is \( 28.26 \) square yards.

Answer:

Circumference: \( 18.84 \) yd
Area: \( 28.26 \) \( \text{yd}^2 \)