Area of a Segment

Q. The area of the sector whose arc subtends an angle of ${90}^{\circ }$ is given as $88{\text{cm}}^2$. Find the area of the segment formed.

1. $32{\text{cm}}^2$
2. $88{\text{cm}}^2$
3. $33{\text{cm}}^2$
4. $56{\text{cm}}^2$

Q. With respect to the area of segment, choose the correct following option.

1. It is the addition of the area of sector and area of triangle.
2. It is the difference between the area of sector and area of triangle.
3. It is the product of the area of sector and area of triangle.
4. None of the above.

Q. William ordered a 6 inch uncut pizza. Gina and Rina cut out slices of the pizza as shown in the figure:

What is the area of the pizza cut out by Gina, Rina and William?

1. Area left for William $=(21\pi +18)inc{h}^2$
   Area cut out by Gina $=6\pi inc{h}^2$
   Area cut out by Rina $=(9\pi -18)inc{h}^2$
2. Area left for William $=(21\pi +18)inc{h}^2$
   Area cut out by Gina $=6\pi -18inc{h}^2$
   Area cut out by Rina $=(9\pi -18)inc{h}^2$
3. Area left for William $=(21\pi +18)inc{h}^2$
   Area cut out by Gina $=6\pi inc{h}^2$
   Area cut out by Rina $=(9\pi +18)inc{h}^2$
4. Area left for William $=(21\pi -18)inc{h}^2$
   Area cut out by Gina $=6\pi inc{h}^2$
   Area cut out by Rina $=(9\pi -18)inc{h}^2$

Q. What will be the area of the segment, if the arc subtends an angle of ${90}^{\circ }$ at the centre of the circle of radius $6\text{cm}$?

1. $9(\pi -2){\text{cm}}^2$
2. $(6\pi -12){\text{cm}}^2$
3. $3(3\pi -1){\text{cm}}^2$
4. $12(3\pi -1){\text{cm}}^2$

Q. Area of the segment $ABC$ given below is:

1. $\frac{2\pi }{3}-\sqrt{3}{\text{cm}}^2$
2. $\frac{2\pi }{3}+\sqrt{3}{\text{cm}}^2$
3. $\frac{\pi }{3}-2\sqrt{3}{\text{cm}}^2$
4. $\frac{\pi }{3}+2\sqrt{3}{\text{cm}}^2$