Question

In the figure 7.31, radius of the circle is 7 cm and m(arcMBN) = 60°,Find
(1) Area of the circle .
(2) A(O - MBN) .
(3) A(O - MCN) .

Answer 1

Answer:

154 cm²

Step-by-step explanation:

Area of circle = π R²

π = 22/7

R = Radius = 7 cm

Area of circle = (22/7) * 7² = 154 cm²

Taking Question text data : m(arcMBN) = 60°

A(O - MBN)  = (60/360) * area of circle

= (1/6) * 154

= 25.67 cm²

A(O - MCN)  = area of circle  - A(O - MBN)

=> A(O - MCN)  = 154- 25.67 = 128.33  cm²

Taking Question image data : m(arcMBN) = 68°

A(O - MBN)  = (68/360) * area of circle

= 29.09 cm²

A(O - MCN)  = area of circle  - A(O - MBN)

=> A(O - MCN)  = 154- 29.09 = 124.91 cm²

Answer 2

Answer:

1. Area of the circle = $\rm 153.938\ cm^2.$
2. A(O - MBN) = $\rm 29.077\ cm^2.$
3. A(O - MCN) = $\rm 124.861\ cm^2.$

Step-by-step explanation:

Given:

• Radius of the circle, R = 7 cm.
• Angle subtended by arc MBN at the center of the circle,  m(arcMBN) = 68°.

(1): To find area of the circle:

The area of is given by,

$\rm Area\ of\ the\ circle=\pi R^2=\pi\times 7^2=153.938\ cm^2.$

(2): To find area of sector (O-MBN) of the circle:

The angle subtended by the whole circle at its center is $360^\circ$ and the area of the whole circle is $\rm \pi R^2$.

The arc (MBN) of the circle is subtending the angle $68^\circ$ at the center of the circle therefore the area of the sector (O-MBN) is given by

$\rm A(O-MBN)=68^\circ\times \dfrac{1}{360^\circ}\pi R^2=\dfrac{68}{360}\times \pi \times 7^2=29.077\ cm^2.$

(3): To find area of sector (O-MCN) of the circle:

It is clear that,

( Area of the whole circle ) = ( Area of sector (O-MBN) of the circle ) + ( Area of sector (O-MCN) of the circle )

Such that,

$\rm Area\ of\ the\ circle = A(O-MBN)+A(O-MCN)\\\Rightarrow A(O-MCN)=( Area\ of\ the\ circle)-A(O-MBN)\\A(O-MCN)=153.938\ cm^2-29.077\ cm^2=124.861\ cm^2.$