Answer to Question #157933 in Civil and Environmental Engineering for Bonevie tutor

Question

Length of an arc

Find the length of an arc of a circle having the radius of 8 cm and subtended by a central angle of 330°.

Find the radius of a circle subtended by a central angle of π/4 radius and having an arc length of π.

On a circle of radius 100 cm, the arc intercepted a central angle of 3π/4. What is the arc length?

Answer 1

a. length of an arc = 2$\pi r(\frac{{1}}{360}\theta)$

$l=$ $2 \times \pi \times 8 \times (\frac{{330}}{360}) = 46. 0767$

$l$ = 46.0767 cm

b.

$\theta$ = $\frac{1}{4}\pi$ = 45$^0$

$l=$ $2 \times \pi \times r \times (\frac{{45}}{360})$

but $l=\pi$

then

$\pi=$ $2 \times \pi \times r \times (\frac{{45}}{360})$

$r= \frac{360}{45 \times2}= 4$

c.

$l=$ $2 \times \pi \times 100\times (\frac{{135}}{360}$ )

$l=$ 75$\pi$