Question

What is the radian measure of the central angle of a circle of radius 1.5 meter that intercepts an arc of length 600 centimeters

Answer 1

Radian measure of the central angle is 4 radian

Solution:

Given that,

A circle of radius 1.5 meter that intercepts an arc of length 600 centimeters

To find: Radian measure of the central angle

Let us find the circumference of circle

The circumference of circle is given as:

$\text{ circumference of circle } = 2 \pi r$

Where "r" is the radius of circle

$\text{ circumference of circle } = 2 \times \pi \times 1.5 = 3 \pi$

Therefore circumference of circle = $3 \pi$ meters , which subtends central angle of  $2 \pi$ radian

Given that arc of length 600 centimeters. Let us convert 600 centimeter to meter

We know that, to convert centimeter to meter divide the length value by 100

$\text{ 600 centimeter } = \frac{600}{100} \text{ meter } = 6 \text{ meter}$

Therefore arc of 6 meter will subtend a central angle of:

$\rightarrow \frac{6}{3 \pi} \times 2 \pi = 4$

Therefore radian measure of the central angle is 4 radian