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

Given that the area of a circular sector is 1/4 of the area of a circle. Find in radians, the central angle, correct to one decimal place.

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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. Itโ€™s one-fourth of a turn, from zero degrees to 90 degrees. Itโ€™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 ๐œ‹ over 180 degrees. That gives us ๐œ‹ over two. 90 degrees is equal to ๐œ‹ over two radians. We want to round this to one decimal place. If we divide ๐œ‹ 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. Weโ€™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.

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