Two semicircles of equal radii are cut out of a semicircle piece of cardboard.Find the area of the shaded portion.(Ans=38.5m^square)
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Two semicircles of equal radii are cut out of a semicircle piece of cardboard.Find the area of the shaded portion.(Ans=38.5m^square)
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[tex] \large\bf\underline{Given:-}[/tex]
[tex] \large\bf\underline {To \: find:-}[/tex]
[tex] \huge\bf\underline{Solution:-}[/tex]
Diameter of Bigger semicircle = 14m
then ,
Now radius of bigger semicircle is the diameter of smaller semicircles.
[tex] \bf \dag \: area \: of \: semicircle = \frac{ \pi \: {r}^{2} }{2} [/tex]
Now,
[tex] \rm \text{Area of bigger semicircle = } \frac{ \frac{22} {7} \times {7}^{2} }{2} \\ \\ \rm \text{Area of bigger semicircle = } \frac{ \frac{22}{ \cancel7} \times \cancel{49}}{2} \\ \\ \rm \text{Area of bigger semicircle = } \frac{22 \times 7}{2} \\ \\ \rm \text{Area of bigger semicircle = } \frac{154}{2} \\ \\ \rm \text{Area of bigger semicircle = }77 {m}^{2} [/tex]
Now ,finding area of smaller semicircles :-
[tex]\rm \text{Area of smaller semicircles = } 2( \frac{ \frac{22}{7} \times (\frac{7}{2} ) {}^{2} }{2}) \\ \\ \rm \text{Area of smaller semicircles = } 2(\frac{ \frac{22}{ \cancel7} \times \frac{ \cancel{49}}{4} }{2} ) \\ \\ \rm \text{Area of smaller semicircles = } 2( \frac{ \frac{11 \times 7}{2} }{2} )\\ \\ \rm \text{Area of smaller semicircles = } 2 (\frac{77}{4} ) \\ \\ \rm \text{Area of smaller semicircles = } \frac{154}{4} \: {m}^{2} [/tex]
Area of shaded region = Area of bigger semicircle - area of both semicircles.
Area of shaded region = 77 - 154/4
Area of shaded region = (308 - 154)/4
Area of shaded region = 154/4
Area of shaded region = 77/2
Step-by-step explanation:
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