Question

What is $8\pi$ in degrees?
(a) 1000
(b) 1200
(c) 1440
(d) None of these

Answer 1

In this problem, we have to find the value of $8\pi$ in degrees. It is also said that $\pi$ radian = 180 degrees. Thus, to find the needed solution, we are to multiply the value in degrees with 8. Simplifying and getting ahead with the problem will give us our needed result.

Complete step by step solution:
According to the problem, we are trying to find the value of 8pi in degrees.
So, to start with, we have $8\pi$ in the given problem.
And again, we know, $\pi$ radian = 180 degrees.
Thus, 8pi radian will tell us, the value of $\pi$ multiplied by 8.
Hence, the value of $8\pi$ radian would be, $\left( 8\times \pi \right)$ .
Now, writing $\pi$ radian equaling 180 degrees, we can write the value as, $\left( 8\times 180{}^\circ \right)=1440{}^\circ$ .
Hence, we have our value of $8\pi$ in degrees as $1440{}^\circ$.
Then, our solution is, (c) 1440.

Note: In the problem, we have used the value of $\pi$ radian. A radian is the measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle. 360° is the whole circle. 180° is half the circle . Radian measure is just a different way of talking about the circle. Radian measure is just a different unit of measure.