Question Video: Finding the Central Angle of a Circular Sector in Radians given a Relation between the Areas of That Sector and the Circle Mathematics

Video Transcript

Given that the area of a circular sector is one-fourth of the area of a circle, find in radians the central angle, correct to one decimal place.

We have a circle, and our circular sector is one-fourth of the area of the total circle. One-fourth of a circle would look like this. And the central angle of this sector is what is shown in pink, here. It’s one-fourth of a turn, from zero degrees to 90 degrees. It’s pretty recognisable. This is 90 degrees. But what is 90 degrees in radians?

To find out, we take our degrees and we multiply it by 𝜋 over 180 degrees. That gives us 𝜋 over two. 90 degrees is equal to 𝜋 over two radians. We want to round this to one decimal place. If we divide 𝜋 by two, we get an irrational number, 1.5707, and it continues without terminating.

Rounding that to one decimal place, we look to the right of the tenths place; there is a seven. We’re going to round the tenths place up to six, and then everything to the left of the six stays the same, one and six-tenths. 90 degrees, a 25 percent turn in our circle, is about one and six-tenths radians.