If chord of a circle of radius 28 cm makes an angle of 90∘at the center, then find out the area of the major segment.

Given that, chord

AB

of a circle of radius 28 cm makes an angle of

90^{\circ}

from the center.

We know that, area of circle =

π r^{2}

and
Area of the sector AOB

= \frac{90^{\circ}}{360^{\circ}} π r^{2}

= \frac{1}{4} π r^{2}

{Area of sector

= \frac{Angle}{360^{\circ}} π r^{2}}

Then from figure,
Area of shaded part = Area of Circle - Area of sector AOB

\Rightarrow

Area of shaded part =

π r^{2} - \frac{1}{4} π r^{2}

\Rightarrow

Area of shaded part =

\frac{3}{4} π r^{2}

\Rightarrow

Area of shaded part

= \frac{3}{4} \times \frac{22}{7} \times 28^{2}

\Rightarrow

Area of shaded part

= 3 \times 22 \times 28

\Rightarrow

Area of shaded part

= 66 \times 28

\Rightarrow Area of shaded part = {1848 cm}^{2}

And area of triangle =

\frac{1}{2} \times b \times h

= \frac{1}{2} \times 28 \times {28 cm}^{2}

= 14 \times {28 cm}^{2}

= {392 cm}^{2}

From figure,
Area of major segment = Area of shaded part + Area of triangle
= 1848 + 392

= {2240 cm}^{2}

Therefore, area of the major segment is

{2240 cm}^{2}

.
Hence, option (4) is correct.

If chord of a circle of radius 28 cm makes an angle of $90^{\circ}$ at the center, then find out the area of the major segment.