Question

Знайдiть градусную мiру дуги кола, довжина якоï дорiвнюе π см, якщо радiус кола дорiвнюе 12см

Answer 1

$\alpha = \dfrac{180а\cdot l}{R\cdot \pi } = \dfrac{180а\cdot \pi }{12\cdot \pi } =15а$

Answer 2

Calculating the Arc Length of a Circle

To find the degree measure of the arc of a circle when the length of the arc is equal to π cm and the radius of the circle is 12 cm, we can use the formula for the arc length of a circle.

The formula for the arc length of a circle is given by:

Arc Length = (θ/360) * 2πr

Where: - θ = angle measure in degrees - r = radius of the circle

We can rearrange the formula to solve for θ:

θ = (Arc Length / (2πr)) * 360

Calculating the Degree Measure

Substituting the given values into the formula:

Arc Length = π cm Radius (r) = 12 cm

We can calculate the degree measure (θ) of the arc:

θ = (π / (2 * π * 12)) * 360

Solving this equation gives us the degree measure of the arc of the circle.