Let r, d, and c be the radius, diameter, and circumference of a circle, respecti

Question

Let r, d, and c be the radius, diameter, and circumference of a circle, respectively. Which of the following statements about “1 rd (radian)” is incorrect?

a. it is the central angle whose opposite arc length equals r

b. it is the central angle whose opposite arc length equals c/(2pi)

c. it is the central angle whose opposite arc length equals d/pi

d. it is the central angle whose opposite arc length equals d/2

The central angle whose opposite arc length equals the circumference of the circle is?

a. 2pi rd

b. 2pi rd

c. 180 degrees

d. 57.3 degrees

e. 90.0 degrees

Explanation / Answer

Ans: c. it is the central angle whose opposite arc length equals d/pi ->>> is incorrect.

If you observe closely, all the other options (a,b,d) are same. All eventually turn out to be r.

a) r is given directly.

b) We know, c = 2pi x r

So, c/2pi = (2pi x r)/2pi = r.

d)We know, d/2 is nothing but r.

____________________________________

Ans: a and b (both options are same)

When opposite arc length equals the circumference, the angle is obviously 360 degrees.

Now, 1 rd = 57.3 degrees

So, 2pi rd = 2pi x 57.3 = 360 degrees

Hope this helps :)

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