Question

Calculate the following quantities:________.

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.