Question

The length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81 degrees. What is the approximate length of the radius of the circle?
A 5.19 units
B 3.51 units
C 11.03 units
D 10.38 units

Answer 1

Answer:

A.  5.19 units

Step-by-step explanation:

$\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle)}$

Given:

• $\theta$ = 81°
• Arc length = 7.34 units

Substituting given values into the equation and solving for r:

$\implies 7.34=2 \pi r\left(\dfrac{81^{\circ}}{360^{\circ}}\right)$

$\implies 7.34=r\left(\dfrac{18 \pi}{40}\right)$

$\implies 7.34 \cdot 40=18 \pi r$

$\implies 293.6=18 \pi r$

$\implies r=\dfrac{293.6}{18 \pi}$

$\implies r=5.19 \sf \: units \:(2\:dp)$

Answer 2

Answer:

A) 5.19 units

Step-by-step explanation:

Formula for arc length :

• arc length = 2πr × θ/360°
• 7.34 = 2 x 22/7 x r x 81/360
• 7.34 = 44/7 x 9/40 x r
• 7.34 = 396/280 x r
• r = 7.34/396 x 280
• r = 280 x 0.0185353535
• r = 5.19 units (approximately)