Question

A circular sidewalk with a radius of 100 meters is having a railing installed

along 120° of its arc. How many meters of railing will be needed? (HINT: arc
length).

A. 100pi/3 m
B. 200pi/3 m
C. 10pi/3 m
D. 2pi/3 m​

Answer 1

B

Explanation:

Whole circle is 360 degrees.

The railing is 120 degrees.

That is:

120/360 = 1/3 rd of the whole length of the circle (perimeter).

We will find perimeter of the circle (a.k.a. Circumference) and then multiply it by (1/3) to get meters of railing needed.

First, circumference:

`C=2\pi r\\C=2 \pi (100)\\C=200\pi\\C=628.32`

The railing is (1/3)rd of it, so:

`(1)/(3)*628.32=209.44`

The railing is 209.44 meters.

The answer choices are in pi, so it will be:

`(1)/(3)*200\pi=(200\pi)/(3)` meters

Answer choice B is right