The given radii of 4 and 6 and the sector angle of 112°, gives;
[tex] C.\: \frac{56 \cdot \pi}{9} [/tex]
The possible figure that relates to the question can be described as follows;
Two concentric circles having radii of AE = 4, and AB = 6, respectively.
Sector of the circles formed by lines AC and AB, with angle of sector = 112°
The shaded portion is described by arcs FE and CB
Therefore;
Area of the sectors are found as follows;
[tex]AFE = \frac{112 ^\circ}{360 ^\circ} \times \pi \times {4}^{2} = \frac{224 \cdot \pi}{45} [/tex]
[tex]ACB = \frac{112 ^\circ}{360 ^\circ} \times \pi \times {6}^{2} = \frac{56 \cdot \pi}{5} [/tex]
Area of the shaded portion, A is therefore;
[tex] A= \frac{56 \cdot \pi}{5} - \frac{224 \cdot \pi}{45} =\frac{56 \cdot \pi}{9} [/tex]
[tex] Shaded \: area, \: A= \frac{56 \cdot \pi}{9} [/tex]
Learn more about the sectors of a circle here:
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