Question

$find \: the \: area \: of \: each \: figure(take\pi = 3.14)$
a) A circle of radius 16 cm
b) A semi circle of diameter 34 cm
c) a quarter circle of radius 50 cm ​

Answer 1

Given :-

a) A circle of radius 16 cm

b) A semi circle of diameter 34 cm

c) a quarter circle of radius 50 cm

To Find :-

• The area of all these shapes by taking ( π = 3.14 )

Solution :-  

❒ Here, we’re given measures of different shapes and we need to find their areas. We can easily find their areas by putting the values in the formulas.  

____________

$\underline{\bf{\dag} \;\; \mathfrak{As\;we\;know\;that:}}$

$\boxed{\sf{ \maltese \;\; Radius = \dfrac{diameter}{2}}}$

$\boxed{\sf{ \maltese \;\; Area\;of\;circle = \pi r^{2} }}$

$\boxed{\sf{ \maltese \;\; Area\;of\;semi-circle = \dfrac{ \pi r^{2}}{2} }}$

$\boxed{\sf{ \maltese \;\; Area\;of\;quarter\;of\;circle = \dfrac{ \pi r^{2}}{4} }}$ 

____________  

Finding the area of circle :-  

$\sf \implies 3.14 \times 16\;cm \times 16 \; cm$ 

$\sf \leadsto \;\; \bigstar \;\; 803.84 \;cm^{2}$

Finding the area of semi-circle :-  

$\sf \implies 3.14 \times \dfrac{34}{2} \times \dfrac{34}{2} \times \dfrac{1}{2}$ 

$\bf {\dag} \;\; \dfrac{34}{2} \; \;is\;taken\;because \\\\we\;are\;given\;diameter$  

$\sf \implies 3.14 \times 17 \times 17 \times 0.5$

$\sf \leadsto \;\; \bigstar \;\; 453.73\;cm^{2}$ 

Finding the area of quarter of circle :-  

$\sf \implies 3.14 \times 50\;cm \times 50\;cm \times \dfrac{1}{4}$  

$\sf \implies 3.14 \times 50\;cm \times 50\;cm \times 0.25$ 

$\sf \leadsto \;\; \bigstar \;\; 1962.5 \;cm^{2}$ 

____________

Hence,  

• Area of circle is 803.84  
• Area of semi-circle is 453.73  
• Area of quarter of circle is 1962.5  

____________

Answer 2

Given :

a) A circle of radius 16 cm

b) A semi circle of diameter 34 cm

c) a quarter circle of radius 50 cm

$\: \: \:$

To find :

The Area of all Shapes

$\: \: \:$

Solution :

$\: \: \:$

${ \bf{ \red{a.)}}} \: \color{blue} {\underline { \boxed{\bf{Area \: of \: Circle = \pi {r}^{2} }}}}$

$\: \: \:$

$\sf : \implies3.14 \times 16 \times 16$

$\: \: \:$

$\sf : \implies803.84 \: {cm}^{2}$

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$\: \: \:$

$\red{ \bf{b.)}} \: \color{blue}{ \underline { \boxed{ \bf{Area \: Of \: Semi \: Circle \: = \dfrac{\pi {r}^{2} }{2} }}}}$

$\: \: \:$

$: \sf\implies3.14 \times \dfrac{34}{2} \times \dfrac{34}{2} \times \dfrac{1}{2}$

$\: \: \:$

$\sf : \implies3.14 \times 17 \times 17\times0.5$

$\: \: \:$

$\sf : \implies453.73 \: {cm}^{2}$

___________________

$\: \: \:$

$\red{\bf{ c.)} } \: \underline{ \boxed{ \color{blue} \bf Area \: of \: Quarter \: Circle = \dfrac{\pi {r}^{2} }{4} }}$

$\: \: \:$

$\sf : \implies3.14 \times 50 \times 50 \times \dfrac{1}{4}$

$\: \: \:$

$\sf : \implies3.1 \times 50 \times 50 \times 0.25$

$\: \: \:$

$\sf : \implies1962.5 \: {cm}^{2}$

___________________

$\: \: \:$