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 \\) in\\(^2\\)
b.
\\( c= \square \\) cm
\\( a= \square \\) cm\\(^2\\)
c.
\\( c= \square \\) cm
\\( a = \square \\) 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 Radius (r) for Area

The radius \( r = \frac{d}{2} = \frac{12}{2} = 6 \) in

Step3: Find Area (A)

The formula for the area of a circle is \( A = \pi r^2 \)
\( A = 3.14 \times 6^2 \)
\( A = 3.14 \times 36 \)
\( A = 113.04 \) \( \text{in}^2 \)

Part b

Step1: Find Circumference (C)

Using \( C = \pi d \), where \( d = 22 \) cm and \( \pi = 3.14 \)
\( C = 3.14 \times 22 \)
\( C = 69.08 \) cm

Step2: Find Radius (r) for Area

\( r = \frac{d}{2} = \frac{22}{2} = 11 \) cm

Step3: Find Area (A)

Using \( A = \pi r^2 \)
\( A = 3.14 \times 11^2 \)
\( A = 3.14 \times 121 \)
\( A = 379.94 \) \( \text{cm}^2 \)

Part c

Step1: Find Circumference (C)

The formula for circumference can also be \( C = 2\pi r \), where \( r = 12 \) cm and \( \pi = 3.14 \)
\( C = 2 \times 3.14 \times 12 \)
\( C = 75.36 \) cm

Step2: Find Area (A)

Using \( A = \pi r^2 \)
\( A = 3.14 \times 12^2 \)
\( A = 3.14 \times 144 \)
\( A = 452.16 \) \( \text{cm}^2 \)

Answer:

s:

Part a

• \( C = \boldsymbol{37.68} \) in
• \( A = \boldsymbol{113.04} \) \( \text{in}^2 \)

Part b

• \( C = \boldsymbol{69.08} \) cm
• \( A = \boldsymbol{379.94} \) \( \text{cm}^2 \)

Part c

• \( C = \boldsymbol{75.36} \) cm
• \( A = \boldsymbol{452.16} \) \( \text{cm}^2 \)