MATH SOLVE

5 months ago

Q:
# What is the radius of a circle in which a 30° arc is 2inches long?24 inchesO 12 incheso 213 inches

Accepted Solution

A:

Answer:The radius of the circle is 12 inches.Step-by-step explanation:Given:The radius of a circle in which a 30° arc is 2π.Now, we put the formula of circumference first.[tex]C=2\pi r[/tex]Now, since 30 is one twelfth of 360, a 30° arc will be one twelfth of the whole circumference. So, if you call the arc length A, you have:[tex]A=\frac{C}{12}=\frac{2\pi r}{12}=\frac{\pi r}{6}[/tex]So, we know the arc length, now we can put the value and solve the following equation:[tex]\frac{\pi r}{6}=2\pi[/tex]Multiplying both sides by 6 and then dividing both sides by π we get :[tex]r=12[/tex].Therefore, the radius of the circle is 12 inches.