Question

In a circle, an angle measuring 7π/4 radians intercepts an arc of length 35π/4. Find the radius of the circle in simplest form.

a) 5
b) 7
c) 10
d) 14

Answer 1

The radius of the circle is 0.2, which is equivalent to 1/5. The correct answer is a) 5.

Step-by-step explanation:

To find the radius of the circle, we can use the formula for calculating the circumference of a circle.

The formula is C = 2πr, where C is the circumference and r is the radius. In this case, the angle intercepts an arc of length 35π/4.

Since the angle is given in radians and the arc length is given in terms of π, we can equate the angle to the arc length and solve for the radius. 7π/4 = 35π/4r.

We can simplify the equation to r = 7/35 = 1/5. Therefore, the radius of the circle is 1/5, which is equivalent to 0.2. The correct answer is a) 5.