Question

in the given figure the the radius of the circle is 7cm find the area of the segment pqr
8th question

Answer 1

Area of sector POR=( theta/360) *pi*r * r
Therefore, area of sector POR= 30/360 *22/7 *7*7
= 1/12* 22* 7
= 77/6
Area Of segment PQR= area of sector- area of triangle POR= 77/6 - 1/2* r* r*sin 30
= 77/6 - 49/2* 1/2
= 77/6 -49/4
= 7/12 cm2

Answer 2

GIVEN,

radius= 7cm

TO FIND,

Area of the segment.

SOLUTION,

let

We know that,

area of the sector POR=  $\frac{theta}{360\\}$*π* R²

substituting the values, we get,

AREA OF SECTOR= $\frac{30}{360} *\frac{22}{7} * 7^{2}$

                              = $\frac{1}{12} *22*7\\\\=\frac{77}{6}$

now the area of the segment PQR

= area of the sector- the area of triangle POR

= $\frac{77}{6} - \frac{1}{2} * r^{2} sin 30$

=$\frac{77}{6} -\frac{49}{2} *\frac{1}{2}$

simplifying,

=$=\frac{77}{6} -\frac{49}{4} \\\\=\frac{7}{12} cm^{2}$

HENCE THE AREA OF THE SEGMENT PQR IS  $\frac{7}{12} cm^{2}$.