Question

use the diameter (d) or radius (r) of each circle to find the circumference (c) and area (a) of the circle. use 3.14 for π. round answers to the nearest hundredth (if necessary). each time an answer appears in the coded title, write the letter of the exercise above it. 1. r = _ in. c = _ in. a = _ in.² 2. d = _ m c = _ m a = _ m² 3. d = 80 ft c r = _ ft u c = _ ft w a = _ ft² 4. r = 18 in. s d = _ in. l c = _ in. k a = _ in.² 5. d = 1.4 cm e r = _ cm t c = _ cm q a = _ cm² 6. r = 7.5 mm f d = _ mm n c = _ mm r a = _ mm²

Explanation:

Step1: Find radius, circumference and area for circle 1

• Radius ($r$):

The formula for the radius of a circle is \(r=\frac{d}{2}\), where \(d\) is the diameter. Given \(d = 6\) in, then \(r=\frac{6}{2}=3\) in.

• Circumference ($C$):

The formula for the circumference of a circle is \(C=\pi d\). Using \(\pi = 3.14\) and \(d = 6\) in, we have \(C=3.14\times6 = 18.84\) in.

• Area ($A$):

The formula for the area of a circle is \(A=\pi r^{2}\). Since \(r = 3\) in, \(A=3.14\times3^{2}=3.14\times9 = 28.26\) in².

Step2: Find diameter, circumference and area for circle 2

• Diameter ($d$):

The formula for the diameter of a circle is \(d = 2r\). Given \(r=2.6\) m, then \(d=2\times2.6 = 5.2\) m.

• Circumference ($C$):

Using the formula \(C=\pi d\) with \(d = 5.2\) m and \(\pi=3.14\), we get \(C=3.14\times5.2=16.328\approx16.33\) m.

• Area ($A$):

Using the formula \(A=\pi r^{2}\) with \(r = 2.6\) m, \(A=3.14\times(2.6)^{2}=3.14\times6.76 = 21.2264\approx21.23\) m².

Step3: Find radius, circumference and area for circle 3

• Radius ($r$):

Given \(d = 80\) ft, using \(r=\frac{d}{2}\), we have \(r=\frac{80}{2}=40\) ft.

• Circumference ($C$):

Using \(C=\pi d\) with \(d = 80\) ft and \(\pi = 3.14\), \(C=3.14\times80=251.2\) ft.

• Area ($A$):

Using \(A=\pi r^{2}\) with \(r = 40\) ft, \(A=3.14\times40^{2}=3.14\times1600 = 5024\) ft².

Step4: Find diameter, circumference and area for circle 4

• Diameter ($d$):

Given \(r = 18\) in, using \(d = 2r\), we get \(d=2\times18 = 36\) in.

• Circumference ($C$):

Using \(C=\pi d\) with \(d = 36\) in and \(\pi=3.14\), \(C=3.14\times36 = 113.04\) in.

• Area ($A$):

Using \(A=\pi r^{2}\) with \(r = 18\) in, \(A=3.14\times18^{2}=3.14\times324 = 1017.36\) in².

Step5: Find radius, circumference and area for circle 5

• Radius ($r$):

Given \(d = 1.4\) cm, using \(r=\frac{d}{2}\), we have \(r=\frac{1.4}{2}=0.7\) cm.

• Circumference ($C$):

Using \(C=\pi d\) with \(d = 1.4\) cm and \(\pi=3.14\), \(C=3.14\times1.4 = 4.396\approx4.40\) cm.

• Area ($A$):

Using \(A=\pi r^{2}\) with \(r = 0.7\) cm, \(A=3.14\times0.7^{2}=3.14\times0.49 = 1.5386\approx1.54\) cm².

Step6: Find diameter, circumference and area for circle 6

• Diameter ($d$):

Given \(r = 7.5\) mm, using \(d = 2r\), we get \(d=2\times7.5=15\) mm.

• Circumference ($C$):

Using \(C=\pi d\) with \(d = 15\) mm and \(\pi=3.14\), \(C=3.14\times15 = 47.1\) mm.

• Area ($A$):

Using \(A=\pi r^{2}\) with \(r = 7.5\) mm, \(A=3.14\times(7.5)^{2}=3.14\times56.25 = 176.625\approx176.63\) mm².

Answer:

1. \(r = 3\) in, \(C=18.84\) in, \(A = 28.26\) in²; 2. \(d = 5.2\) m, \(C\approx16.33\) m, \(A\approx21.23\) m²; 3. \(r = 40\) ft, \(C = 251.2\) ft, \(A = 5024\) ft²; 4. \(d = 36\) in, \(C = 113.04\) in, \(A = 1017.36\) in²; 5. \(r = 0.7\) cm, \(C\approx4.40\) cm, \(A\approx1.54\) cm²; 6. \(d = 15\) mm, \(C = 47.1\) mm, \(A\approx176.63\) mm².