Question

the circular portions of the following figures are semicircles.For each of the following figures, find its perimeter and area
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its important
hurry answer is 56.5cm and 191cm²
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Answer 1

There are three semicircles in the figure.

Let the radius for the bigger semicircle be R and fir the two smaller circle be r1 and r2.

Now,

$\boxed{ \underline{ \gray{ \sf{Perimeter \: of \: semi-circle \: = \frac{1}{2} \pi r \: + 2r }}}}$

$\boxed{ \underline{ \gray{ \sf{Area \: of \: semi - circle = \frac{\pi {r}^{2} }{ 2 } }}}}$

Diameter of bigger circle = 18 cm

$\sf \therefore \: Radius = \dfrac{18}{2} \implies \: 9cm$

$\sf \: Perimeter = \dfrac{1}{2} \pi r \: + \: 2r \\ \\ \sf \: = \: \frac{1}{ \cancel2} \times \frac{ \cancel{22} \: ^{11} }{7} \times 9 + 2 \times 9 \\ \\ \sf \: = \: \frac{99}{7} + 18 \\ \\ \sf \: = \: \frac{99 + 126}{7} \\ \\ \: = \: \boxed{ \sf \: \frac{225}{7} cm}$

$\sf \: Area \: of \: the \: bigger \: semicircle = \dfrac{\pi {r}^{2} }{2} \\ \sf \: = \frac{ \frac{22}{7} \times {9}^{2} }{2} \\ \\ \sf \: = \frac{22 \times 81}{7} \times \frac{2}{1} \\ \\ \: = \boxed{ \sf{ \frac{3564}{7} {cm}^{2} }}$

Now,

Diameter of the 1st small circle = 9 cm

Diameter of the 2nd small circle = 9cm

$\sf \: \therefore \: Radius \: of \: the \: two \: semicircles= \frac{9}{2} \\ \sf \implies4.5 \: cm$

$\sf \: Perimeter \: of \: the \: 1st \: small \: semicircle = \dfrac{1}{2} \pi r1 \: + \: 2r2 \\ \\ \sf \: = \: \frac{1}{2} \times \frac{22}{7} \times 4.5 + 2 \times 4.5 \\ \\ \sf \: = \: \frac{1}{ \cancel2} \times \frac{ \cancel{22} \: ^{11} }{7} \times \frac{ \cancel{45} \: ^{9} }{ \cancel{10} \: ^{2} } + \cancel2 \times \frac{ \cancel{45} \: ^{9} }{ \cancel{10} \: ^{ \cancel5} } \\ \\ \sf \: = \: \frac{99}{14} + 9 \\ \\ \sf \: = \: \frac{99 + 126}{14} \\ \\ \: = \: \boxed{ \sf{\frac{225}{14} cm}}$

$\sf \: Area \: of \: 1st \: smaller \: circle = \frac{\pi {r}^{2} }{2} \\ \sf \: = \frac{ \frac{22}{7} \times ({4.5})^{2} }{2} \\ \\ \sf \: = \frac{ \frac{22}{7} \times \frac{45}{10} \times \frac{45}{10} }{2} \\ \\ \sf \: = \frac{ \cancel{22} ^{11} }{7} \times \frac{ \cancel{45} \: ^{9} }{ \cancel{10} \: ^{ \cancel2} } \times \frac{ \cancel{45} \: ^{9} }{ \cancel{10} \: ^{ \cancel5} } \times \frac{ \cancel2}{1} \\ \\ \: = \boxed{ \sf{\frac{891}{7} {cm}^{2} }}$

Since, the radius of the two small semicircles are same, therefore the perimeter and area of the two small semicircles will be same.

$\sf \: Perimeter \: of \: the \: 2nd \: small \: semicircle = \dfrac{225}{14} cm$

$\sf \: Area \: of \: the \: 2nd \: small \: semicircle = \dfrac{891}{7} {cm}^{2}$

Now,

Perimeter of the figure = Perimeter of bigger circle + Perimeter of the 1st small semi circle + Perimeter of the 2nd small semi circle

$\sf \: = \: \dfrac{225}{7} + \dfrac{225}{14} + \dfrac{225}{14} \\ \\ \sf \: = \frac{225}{7} + \frac{450}{14} \\ \\ \sf \: = \frac{450 + 450}{14} \implies \: \frac{900}{14} cm \: \: \red{=>56.5 cm}$

And,

Area of the figure = Area of the bigger semicircle + Area of 1st semicircle + Area of 2nd semicircle

$\sf \: = \: \frac{3564}{7} + \frac{891}{7} + \frac{891}{7} \\ \\ \sf \: = \frac{3564 + 891 + 891}{7} \\ \\ \sf \: = \frac{5346}{7} {cm}^{2} \: \: \: \red{\implies{ \:763.71 {cm}^{2} }}$

Answer 2

Answer:

There are three semicircles in the figure.

There are three semicircles in the figure.Let the radius for the bigger semicircle be R and fir the two smaller circle be r1 andr2

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}}

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle=

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 2

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r Area of semi - circle {r}^{2} }{ 2 }

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r Area of semi - circle {r}^{2} }{ 2 }Areaofsemi−circle=

Perimeter of semi-circle = \frac{1}{2} \pi r \: + 2r }}}} Perimeterofsemi−circle= 21 πr+2r Area of semi - circle {r}^{2} }{ 2 }Areaofsemi−circle= 2 πr

πr 2

πr 2

πr 2

πr 2

πr 2

πr 2

πr 2

πr 2

πr 2 Diameter of bigger circle = 18 cm

πr 2 Diameter of bigger circle = 18 cm\therefore \: Radius ={18}{2} implies 9cm∴Radius= ?

answer ⟹

⟹ ⟹763.71cm

⟹ ⟹763.71cm 2

⟹ ⟹763.71cm 2

⟹ ⟹763.71cm 2