Question

pre algebra #7
exercises: find the circumference of each circle below. use \\( \pi=3.14 \\). \\( c=\pi \cdot d \\)
1.)

\\( d=4.2 \mathrm{~m} \\).

circumference = \\( \mathrm{m} \\).

2.)

radius \\( =11.2 \mathrm{~cm} \\).

circumference = \\( \mathrm{cm} \\).

3.) radius \\( =8 \\) meters
circumference = \\( \mathrm{m} \\).

4.) diameter \\( =90 \mathrm{~mm} \\).
circumference = \\( \mathrm{mm} \\).

5.) find the approximate distance around the earths equator if the diameter of the earth is about 12,800 kilometers.
\\( \mathrm{c}= \\) \\( \mathrm{km} \\).

6.) the tree with the greatest known diameter is in mexico. the diameter of the tree is 10.9 meters. find the circumference of the tree to the nearest meter.
\\( \mathrm{c}= \mathrm{m} \\).

use \\( \pi=\frac{22}{7} \\) to find the circumference of each of the following. \\( c=\pi \cdot d \\)
7.)

diameter \\( =5 \frac{1}{4} \\) in.
\\( \mathrm{c}= \\)

8.)

radius \\( =14 \mathrm{~cm} \\).
\\( \mathrm{c}= \\)

Explanation:

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \(C = \pi d\) (where \(d\) is the diameter) or \(C = 2\pi r\) (where \(r\) is the radius).

Step2: Solve problem 1

Given \(d = 4.2m\) and \(\pi=3.14\). Using \(C=\pi d\), we substitute the values: \(C = 3.14\times4.2\).

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Step3: Solve problem 2

Given \(r = 11.2cm\). First, find \(d = 2r=2\times11.2 = 22.4cm\). Using \(C=\pi d\) with \(\pi = 3.14\), \(C=3.14\times22.4\).

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Step4: Solve problem 3

Given \(r = 8m\). Find \(d = 2r = 16m\). Using \(C=\pi d\) with \(\pi=3.14\), \(C=3.14\times16=(3 + 0.14)\times16=48+2.24 = 50.24m\).

Step5: Solve problem 4

Given \(d = 90mm\) and \(\pi=3.14\). Using \(C=\pi d\), \(C=3.14\times90=(3+0.14)\times90 = 270+12.6=282.6mm\).

Step6: Solve problem 5

Given \(d = 12800km\) and \(\pi=3.14\). Using \(C=\pi d\), \(C=3.14\times12800=(3+0.14)\times12800=3\times12800+0.14\times12800=38400 + 1792=40192km\).

Step7: Solve problem 6

Given \(d = 10.9m\) and \(\pi=3.14\). Using \(C=\pi d\), \(C=3.14\times10.9=(3+0.14)\times10.9=3\times10.9+0.14\times10.9=32.7+1.526 = 34.226\approx34m\) (to the nearest meter).

Step8: Solve problem 7

Given \(d = 5\frac{1}{4}=\frac{21}{4}in\) and \(\pi=\frac{22}{7}\). Using \(C=\pi d\), \(C=\frac{22}{7}\times\frac{21}{4}=\frac{22\times21}{7\times4}=\frac{22\times3}{4}=\frac{66}{4}=16.5in\).

Step9: Solve problem 8

Given \(r = 14cm\). Find \(d = 2r=28cm\). Using \(C=\pi d\) with \(\pi=\frac{22}{7}\), \(C=\frac{22}{7}\times28=22\times4 = 88cm\).

Answer:

1. \(13.188m\)
2. \(70.336cm\)
3. \(50.24m\)
4. \(282.6mm\)
5. \(40192km\)
6. \(34m\)
7. \(16.5in\)
8. \(88cm\)