Question

Calculate the circumference of the circles with the following dimensions.C = circumferenceD = diameterR = radiusPI = 3.141. D = 4 in D = 6 in D = 12 in2. R = 2 ft R = 14 ft R = 12 ft3. R = 9 ft R = 11 ft R = 7 ft4. D = 10 ft R = 9 ft D = 13 ft5. Application: Dana is planning to ride her bicycle around the circular race track and wants to know the distance. If the diameter of the track is 2 mile, how far is the distance around the race track?

Answer 1

The formula for calculating the circumference of a circle is given by;

`\begin{gathered} C=2\pi R\ldots\ldots\ldots\ldots.......\ldots\ldots\ldots\text{......}\mathrm{}(\text{when the radius is given)} \\ \\ OR \\ \\ C=\pi D\ldots\ldots\ldots....\ldots\ldots....\ldots\ldots\ldots\ldots\ldots\text{.......}\mathrm{}(\text{when the diameter is given)} \end{gathered}`

Question 1:

`\begin{gathered} when \\ D=4in,\pi=3.14 \\ C=\pi D \\ C=3.14*4 \\ C=12.56in \\ \\ \\ D=6in,\pi=3.14 \\ C=\pi D \\ C=3.14*6 \\ C=18.84in \\ \\ \\ \\ D=12in,\pi=3.14 \\ C=\pi D \\ C=3.14*12 \\ C=37.68in \end{gathered}`

Question 2:

`\begin{gathered} \text{when} \\ R=2ft,\pi=3.14 \\ C=2\pi R \\ C=2*3.14*2 \\ C=18.84ft \\ \\ \\ R=14ft,\pi=3.14 \\ C=2\pi R \\ C=2*3.14*14 \\ C=87.92ft \\ \\ \\ \\ R=12ft,\pi=3.14 \\ C=2\pi R \\ C=2*3.14*12 \\ C=75.36ft \end{gathered}`

Question 3:

`\begin{gathered} \text{when} \\ R=9ft,\pi=3.14 \\ C=2\pi R \\ C=2*3.14*9 \\ C=56.52ft \\ \\ \\ R=11ft,\pi=3.14 \\ C=2\pi R \\ C=2*3.14*11 \\ C=69.08ft \\ \\ \\ \\ R=7ft,\pi=3.14 \\ C=2\pi R \\ C=2*3.14*7 \\ C=43.96ft \end{gathered}`

Question 4:

`\begin{gathered} when \\ D=10ft,\pi=3.14 \\ C=\pi D \\ C=3.14*10 \\ C=31.4ft \\ \\ \\ R=9ft,\pi=3.14 \\ C=2\pi R \\ C=2*3.14*9 \\ C=56.52ft \\ \\ \\ \\ D=13ft,\pi=3.14 \\ C=\pi D \\ C=3.14*13 \\ C=40.82ft \end{gathered}`

Question 5:

The circular track represents a circle.

Given:

`D=2\text{miles}`

The distance around the track represents the circumference of the circular track.

Hence, we find the circumference using the formula below;

`\begin{gathered} C=\pi D \\ C=3.14*2 \\ C=6.28\text{miles} \end{gathered}`

Therefore, the distance around the race track is 6.28 miles