Respuesta :
Solution:
We know that:
[tex]\large\tex\text{Circumference of circle} = 2\pi r = 35 \dfrac{13}{21} \ \tex\text{inches}[/tex]
[tex]\large \pi = \dfrac{22}{7}[/tex]
Somehow, we need to find the radius of the circle. To do that, we need to isolate 'r'.
Isolating 'r':
To isolate "r", we need to divide both sides by 2, then divide both sides by 22/7. You can also multiply 22/7 and 2 and then divide the result both sides to isolate "r".
Step-1: Divide both sides by 2.
[tex]2\pi r = 35 \dfrac{13}{21} \ \tex\text{inches} \\\\\\\ \dfrac{2\pi r}{2} = 35 \dfrac{13}{21} \div 2 \\\\\\ \pi r = \dfrac{35 \times 21 + 13}{21} \div 2 \\\\\\\pi r = \dfrac{748}{21} \times \dfrac{1}{2} \\\\\\\ \pi r = \dfrac{374}{21}[/tex]
Step-2: Divide π both sides.
[tex]\dfrac{\pi r}{\pi} = \dfrac{374}{21} \div \pi \\\\\\ r = \dfrac{374}{21} \div \dfrac{22}{7} \\\\\\ r = \dfrac{374}{21} \times \dfrac{7}{22} \\\\\\ r = \dfrac{17}{3}[/tex]
Now, let's multiply the radius by 2 to obtain the diameter.
Obtaining the diameter:
[tex]\tex\text{Diameter = 2(Radius)} \\\\\\ \tex\text{Diameter} = 2(\dfrac{17}{3} ) \\\\\\ \boxed{\bold{Diameter = \dfrac{34}{3}}}[/tex]
[tex]\\ \rm\rightarrowtail \pi d=35\dfrac{13}{21}[/tex]
- d is diameter
[tex]\\ \rm\rightarrowtail \pi d=\dfrac{748}{21}[/tex]
[tex]\\ \rm\rightarrowtail d=748/21\pi[/tex]
[tex]\\ \rm\rightarrowtail d=11.34in[/tex]
