Respuesta :
Answer:
Radius = 7.17 inches
Explanation:
Circular Sector
The ratio between the sector's area and the circle area equals to the ratio between the sector's arc length and the circle's circumference, also equals to the ratio between the sector's angle and the circle's angle (2π or 360°).
[tex]\displaystyle\frac{sector's\ area}{circle's\ area}=\frac{sector's\ length}{circle's\ circumference}=\frac{sector's\ angle}{circle's\ angle}[/tex]
If we replace the circle's area, circumference and angle with the formula:
[tex]\boxed{\frac{sector's\ area}{\pi r^2}=\frac{sector's\ length}{2\pi r}=\frac{sector's\ angle}{2\pi\ or\ 360^o}}[/tex]
Given:
sector's arc length = 2.5"
sector's angle = 20°
[tex]\displaystyle \frac{sector's\ length}{2\pi r} =\frac{sector's\ angle}{360^o}[/tex]
[tex]\displaystyle\frac{2.5}{2(3.14) r} =\frac{20^o}{360^o}[/tex]
[tex]\displaystyle r=\frac{2.5(360^o)}{2(3.14)(20^o)}[/tex]
[tex]\bf r=7.17"[/tex]
Final answer:
The radius of a bicycle wheel, with segments 20 degrees apart and each segment measuring 2.5 inches, can be estimated to be approximately 7.07 inches. This is calculated using the formula for the circumference of a circle. The correct answer is B) 7.07 inches.
Explanation:
The radius of a bicycle wheel when given the distance between two points on the tire that are 20 degrees apart. To calculate the radius, we need to understand that the circumference of a circle is divided into 360 degrees. Since the spokes are 20 degrees apart, there are a total of 18 segments (360/20) creating 18 arcs around the wheel. The length of one arc (between two spokes) is given as 2.5 inches. The total circumference is, therefore, 2.5 inches multiplied by 18. The formula to find the circumference (C) of a cycle is C = 2πR (where R is the radius).
We can now equate the total circumference to the formula for circumference and solve for R:
2.5 inches * 18 segments = 2πR
45 inches = 2πR
rac{45 inches} {2π} = R
R ≈ 7.16 inches
Thus, the closest answer from the options provided is B) 7.07 inches.
