Question

find the circumference and area of each circle. use 3.14 for $\pi$ and round your answer to the nearest hundredth. (two decimal places.)
a.
$c=\square$ in.
$a=\square$ $\text{in}^2$
b.
$c=\square$ cm
$a=\square$ $\text{cm}^2$
c.
$c=\square$ cm
$a=\square$ $\text{cm}^2$

Explanation:

Part a

Step1: Find Circumference (C)

The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter. Here, \( d = 12 \) in and \( \pi = 3.14 \).
\( C = 3.14 \times 12 \)
\( C = 37.68 \) in.

Step2: Find Area (A)

The formula for the area of a circle is \( A = \pi r^2 \), where \( r \) is the radius. The radius \( r=\frac{d}{2}=\frac{12}{2} = 6 \) in.
\( A = 3.14 \times 6^2 \)
\( A = 3.14 \times 36 \)
\( A = 113.04 \) \( \text{in}^2 \).

Part b

Step1: Find Circumference (C)

The diameter \( d = 22 \) cm. Using \( C=\pi d \) with \( \pi = 3.14 \).
\( C = 3.14\times22 \)
\( C = 69.08 \) cm.

Step2: Find Area (A)

Radius \( r=\frac{d}{2}=\frac{22}{2}=11 \) cm. Using \( A = \pi r^2 \).
\( A = 3.14\times11^2 \)
\( A = 3.14\times121 \)
\( A = 379.94 \) \( \text{cm}^2 \).

Part c

Step1: Find Circumference (C)

The radius \( r = 12 \) cm. The formula for circumference is also \( C = 2\pi r \).
\( C = 2\times3.14\times12 \)
\( C = 75.36 \) cm.

Step2: Find Area (A)

Using \( A=\pi r^2 \) with \( r = 12 \) cm.
\( A = 3.14\times12^2 \)
\( A = 3.14\times144 \)
\( A = 452.16 \) \( \text{cm}^2 \).

Answer:

Part a

Circumference: \( 37.68 \) in, Area: \( 113.04 \) \( \text{in}^2 \)

Part b

Circumference: \( 69.08 \) cm, Area: \( 379.94 \) \( \text{cm}^2 \)

Part c

Circumference: \( 75.36 \) cm, Area: \( 452.16 \) \( \text{cm}^2 \)