Question

circumference & area of a circle
circumference
$c = 2\timespi\times r$
$r = 5cm$
$piapprox3.14$
$c = 2\times3.14\times5cm$
$c = 31.40cm$
area
$a=pi r^{2}$
$r = 5cm$
$piapprox3.14$
$a = 3.14\times(5cm\times5cm)$
$a = 3.14\times25cm^{2}$
$a = 78.50cm^{2}$
find the circumference and area of each circle. use 3.14 for pi.
a.
$c=$
$a=$
b.
$c=$
$a=$
c.
$c=$
$a=$
d.
$c=$
$a=$
e.
$c=$
$a=$
f.
$c=$
$a=$
find the missing measurements.
g. $r = 15cm,d = $, $c = 94.20cm,a = $
h. $r = $, $d = 24mm,c = $, $a = 452.16mm^{2}$
i. $r = 19cm,d = $, $c = $, $a = $

Explanation:

Step1: Calculate circumference and area for a

• Circumference:

Using the formula \(C = 2\pi r\), with \(r = 13\) ft and \(\pi=3.14\).
\(C=2\times3.14\times13 = 81.64\) ft.

• Area:

Using the formula \(A=\pi r^{2}\), with \(r = 13\) ft and \(\pi = 3.14\).
\(A=3.14\times13^{2}=3.14\times169 = 530.66\) \(ft^{2}\).

Step2: Calculate circumference and area for b

• Find radius:

Given \(d = 40\) m, \(r=\frac{d}{2}=20\) m.

• Circumference:

Using \(C = 2\pi r\), \(C=2\times3.14\times20=125.6\) m.

• Area:

Using \(A=\pi r^{2}\), \(A = 3.14\times20^{2}=3.14\times400=1256\) \(m^{2}\).

Step3: Calculate circumference and area for c

• Circumference:

Using \(C = 2\pi r\), with \(r=\frac{15}{2}\) in (\(r = 7.5\) in) and \(\pi=3.14\).
\(C=2\times3.14\times7.5 = 47.1\) in.

• Area:

Using \(A=\pi r^{2}\), \(A=3.14\times7.5^{2}=3.14\times56.25 = 176.625\) \(in^{2}\).

Step4: Calculate circumference and area for d

• Find radius:

Given \(d = 62\) in, \(r=\frac{d}{2}=31\) in.

• Circumference:

Using \(C = 2\pi r\), \(C=2\times3.14\times31=194.68\) in.

• Area:

Using \(A=\pi r^{2}\), \(A=3.14\times31^{2}=3.14\times961 = 3017.54\) \(in^{2}\).

Step5: Calculate circumference and area for e

• Find radius:

Given \(d = 54\) cm, \(r=\frac{d}{2}=27\) cm.

• Circumference:

Using \(C = 2\pi r\), \(C=2\times3.14\times27 = 169.56\) cm.

• Area:

Using \(A=\pi r^{2}\), \(A=3.14\times27^{2}=3.14\times729=2289.06\) \(cm^{2}\).

Step6: Calculate circumference and area for f

• Circumference:

Using \(C = 2\pi r\), with \(r = 17\) m and \(\pi=3.14\).
\(C=2\times3.14\times17=106.76\) m.

• Area:

Using \(A=\pi r^{2}\), \(A=3.14\times17^{2}=3.14\times289 = 907.46\) \(m^{2}\).

Step7: Calculate missing values for g

• Find diameter:

Given \(r = 15\) cm, \(d = 2r=30\) cm.

• Find area:

Using \(A=\pi r^{2}\), with \(r = 15\) cm and \(\pi=3.14\).
\(A=3.14\times15^{2}=3.14\times225 = 706.5\) \(cm^{2}\).

Step8: Calculate missing values for h

• Find radius:

Given \(d = 24\) mm, \(r=\frac{d}{2}=12\) mm.

• Find circumference:

Using \(C = 2\pi r\), \(C=2\times3.14\times12 = 75.36\) mm.

Step9: Calculate missing values for i

• Find diameter:

Given \(r = 19\) cm, \(d = 2r = 38\) cm.

• Find circumference:

Using \(C=2\pi r\), \(C=2\times3.14\times19=119.32\) cm.

• Find area:

Using \(A=\pi r^{2}\), \(A=3.14\times19^{2}=3.14\times361=1133.54\) \(cm^{2}\).

Answer:

a. \(C = 81.64\) ft, \(A = 530.66\) \(ft^{2}\)
b. \(C = 125.6\) m, \(A = 1256\) \(m^{2}\)
c. \(C = 47.1\) in, \(A = 176.625\) \(in^{2}\)
d. \(C = 194.68\) in, \(A = 3017.54\) \(in^{2}\)
e. \(C = 169.56\) cm, \(A = 2289.06\) \(cm^{2}\)
f. \(C = 106.76\) m, \(A = 907.46\) \(m^{2}\)
g. \(d = 30\) cm, \(A = 706.5\) \(cm^{2}\)
h. \(r = 12\) mm, \(C = 75.36\) mm
i. \(d = 38\) cm, \(C = 119.32\) cm, \(A = 1133.54\) \(cm^{2}\)