Question

Calculate the following quantities:________.
a) the angle (in radians) subtended by a circular arc that is 1.50 m long with a radius of 2.50 m
b) the radius of a circle that has an arc 14.0 cm long that subtends an angle of 128o
c) the length of an arc that subtends an angle of 0.700 rad on the circumference of a circle with radius 1.50 m

Answer 1

Answer:

(a) 0.6 radians

(b) 6.27 cm

(c) 1.05 m

Explanation:

(a) The length of an arc is given as:

s = rθ

where r = radius of the circle

θ = angle subtended by the arc (in radians)

Therefore, the angle, θ, will be:

θ = $\frac{s}{r}$

θ = $\frac{1.5}{2.5}$

θ = 0.6 radians

The angle subtended by the circular arc is 0.6 radians.

(b) Using the same formula, we have that radius, r, is given as:

r = s/θ

But θ is in radians and the angle we have is in degrees (128°). Hence, we convert 128° to radians:

128° = $128 * \frac{\pi }{180}$ radians = 2.234 radians

Therefore, r is:

r = 14/2.234

r = 6.27 cm

The radius of the circle is 6.27 cm.

(c) Using the same formula, we have that:

s = rθ

s = 1.5 * 0.7

s = 1.05 m

The length of the arc is 1.05 m.