Chapter 55, Problem 11A

To determine

(a)

The value of circumference of circle.

Answer to Problem 11A

The circumference of circle is $C=20.420"$.

Explanation of Solution

Given information:

The diameter given is d = 6.500"

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the circumference of the circle,

  $\begin{array}{l}\text{Putting the value of diameter in the above equation }\\ C=\pi \times 6.500\\ C=20.420"\end{array}$

The circumference of the circle is $C=20.420".$

Conclusion:

Thus, the circumference of the circle is $C=20.420".$

To determine

(b)

The value of circumference of circle.

Answer to Problem 11A

The circumference of circle is $C=94.247\text{mm}$.

Explanation of Solution

Given information:

The diameter given is d = 30.000 mm

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the circumference of the circle,

  $\begin{array}{l}\text{Putting the value of diameter in the equation }\\ C=\pi \times 30.000\\ C=94.247\text{mm}\end{array}$

The circumference of the circle is $C=94.247\text{mm}\text{.}$

Conclusion:

Thus, the circumference of the circle is $C=94.247\text{mm}\text{.}$

To determine

(c)

The value of circumference of circle.

Answer to Problem 11A

The circumference of circle is $C=116.867\text{mm}$.

Explanation of Solution

Given information:

The radius given is r = 18.600 mm

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the circumference of the circle,

  $\begin{array}{l}\text{Putting the value of diameter in the equation }\\ C=2\pi r\\ C=2\times \pi \times 18.600\\ C=116.867\text{mm}\end{array}$

The circumference of the circle is $C=116.867\text{mm}\text{.}$

Conclusion:

Thus, the circumference of the circle is $C=116.867\text{mm}\text{.}$

To determine

(d)

The value of circumference of circle.

Answer to Problem 11A

The circumference of circle is $C=18.409"$.

Explanation of Solution

Given information:

The radius given is r = 2.930"

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the circumference of the circle,

  $\begin{array}{l}\text{Putting the value of diameter in the equation }\\ C=2\pi r\\ C=2\times \pi \times 2.930"\\ C=18.409"\end{array}$

The circumference of the circle is $C=18.409".$

Conclusion:

Thus, the circumference of the circle is $C=18.409".$

To determine

(e)

The value of diameter of circle.

Answer to Problem 11A

The diameter of circle is $d=11.140$.

Explanation of Solution

Given information:

The circumference given is C = 35.000"

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the diameter of the circle,

  $\begin{array}{l}\text{Putting the value of circumference in the equation}\\ C=\pi d\\ 35.000=\pi \times d\\ d=\frac{35.000}{\pi }=11.140\\ d=11.140\end{array}$

The diameter of the circle is $d=\mathrm{11.140.}$

Conclusion:

Thus, the diameter of the circle is $d=\mathrm{11.140.}$

To determine

(f)

The value of diameter of circle.

Answer to Problem 11A

The diameter of circle is $d=69.391\text{mm}$.

Explanation of Solution

Given information:

The circumference given is C = 218.000 mm.

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the diameter of the circle,

  $\begin{array}{l}\text{Putting the value of circumference in the equation }\\ C=\pi d\\ 218.000=\pi \times d\\ d=\frac{218.000}{\pi }=69.391\\ d=69.391\text{mm}\end{array}$

The diameter of the circle is $d=69.391\text{mm}\text{.}$

Conclusion:

Thus, the diameter of the circle is $d=69.391\text{mm}\text{.}$

To determine

(g)

The value of radius of circle.

Answer to Problem 11A

The radius of circle is $r=52.043\text{mm}$.

Explanation of Solution

Given information:

The circumference given is C = 327.000 mm.

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the radius of the circle,

  $\begin{array}{l}\text{Putting the value of circumference in the equation }\\ C=2\pi r\\ 327.000=2\pi \times r\\ r=\frac{327.000}{2\pi }=52.043\\ r=52.043\text{mm}\end{array}$

The radius of the circle is $r=52.043\text{mm}\text{.}$

Conclusion:

Thus, the radius of the circle is $r=52.043\text{mm}\text{.}$

To determine

(h)

The value of radius of circle.

Answer to Problem 11A

The radius of circle is $r=1.222"$.

Explanation of Solution

Given information:

The circumference given is C = 7.680".

The circumference of the circle is given by

  $\begin{array}{l}C=2\pi r\\ C=\pi d\end{array}$

Where

  $\begin{array}{l}r=\text{Radius of the circle}\\ d\text{= Diameter of the circle}\end{array}$

To calculate the radius of the circle,

  $\begin{array}{l}\text{Putting the value of circumference in the equation}\\ C=2\pi r\\ 7.680"=2\pi \times r\\ r=\frac{7.680"}{2\pi }=1.222"\\ r=1.222"\end{array}$

The radius of the circle is $r=1.222".$

Conclusion:

Thus, the radius of the circle is $r=1.222".$