Question

geometry
circumference and area of a circle
find the area and the circumference of a circle with diameter 4 ft.
use the value 3.14 for π, and do not round your answers. be sure to include the correct units in your answers.
(there is a circle with diameter 4 ft in the image)
area:
ft ft² ft³
circumference:

Explanation:

Step1: Find the radius

The radius \( r \) of a circle is half of the diameter \( d \). Given \( d = 4 \) ft, so \( r=\frac{d}{2}=\frac{4}{2} = 2 \) ft.

Step2: Calculate the area

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Substitute \( \pi = 3.14 \) and \( r = 2 \) ft into the formula: \( A = 3.14\times(2)^{2}=3.14\times4 = 12.56 \) square feet (\( \text{ft}^2 \)).

Step3: Calculate the circumference

The formula for the circumference \( C \) of a circle is \( C=\pi d \) (or \( C = 2\pi r \)). Substitute \( \pi=3.14 \) and \( d = 4 \) ft into the formula: \( C=3.14\times4=12.56 \) feet (\( \text{ft} \)).

Answer:

Area: \( 12.56 \text{ ft}^2 \)
Circumference: \( 12.56 \text{ ft} \)