Is it true to say that the area of a segment of a circle is less than the area of its corresponding sector? Why?
(B) The statement is false.
$1$. $A$ segment of a circle is the region bounded by a chord and an arc. $A$ sector of a circle is the region bounded by two radii and an arc.
$2$. For a minor segment,the area is indeed less than the area of the corresponding minor sector because the minor segment is a part of the minor sector (the sector includes the triangle formed by the two radii and the chord).
$3$. However,for a major segment,the area is always greater than the area of the corresponding major sector. Therefore,the statement is not universally true.
$1$. $A$ segment of a circle is the region bounded by a chord and an arc. $A$ sector of a circle is the region bounded by two radii and an arc.
$2$. For a minor segment,the area is indeed less than the area of the corresponding minor sector because the minor segment is a part of the minor sector (the sector includes the triangle formed by the two radii and the chord).
$3$. However,for a major segment,the area is always greater than the area of the corresponding major sector. Therefore,the statement is not universally true.
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