Question

Градусна міра дуги дорівнює 20 градусів. Знайдіть радіус кола, якщо довжина цієї дуги дорівнює 4п см. ​

Answer 1

Finding the Radius of a Circle Given the Angle and Arc Length

To find the radius of a circle when the angle of the arc is 20 degrees and the length of the arc is 4π cm, we can use the formula:

Arc Length = Radius × Central Angle

In this case, the central angle is given as 20 degrees and the arc length is 4π cm. Let's substitute these values into the formula and solve for the radius.

4π cm = Radius × 20 degrees

To solve for the radius, we need to convert the angle from degrees to radians, as the formula requires the angle to be in radians. We know that 180 degrees is equal to π radians, so we can convert 20 degrees to radians as follows:

20 degrees × (π radians / 180 degrees) = (20π / 180) radians = (π / 9) radians

Now, let's substitute the converted angle into the formula:

4π cm = Radius × (π / 9) radians

To solve for the radius, we can divide both sides of the equation by (π / 9) radians:

Radius = (4π cm) / (π / 9) radians

Simplifying the expression:

Radius = (4π cm) × (9 / π radians) = 36 cm

Therefore, the radius of the circle is 36 cm.