Question

two concentric circles have radii 3.5 cm and 7 cm respectively find the area between the circle ​

Answer 1

What we have to do ?

As from the above question we come to know that two concentric circles have radii 3.5 cm and 7 cm respectively. So, We have to find the area between the circle.

For that, first we will find out the area of both circles and after that we will subtract one by another. Here we get the answer then.

Let's find it :

We have to know -

${\boxed{\bf{Area \: of \: circle = \pi r^{2} }}}$

For Area of Circle 1 :

$\longrightarrow \tt{Radius = 3.5 cm}$

$\longrightarrow \tt{ \pi = \dfrac{22}{7}}$

$:\implies\sf Area \: of \: circle \: 1 = \pi r^{2}$

$:\implies\sf Area \: of \: circle \: 1 = \dfrac{22}{7} \times (3.5)^{2}$

$:\implies\sf Area \: of \: circle \: 1 = \dfrac{22}{7} \times 3.5 \times 3.5$

$\sf \longrightarrow \: Area \: = {\dfrac{22}{ \cancel{7}^{ \: \: 1} } \: \times 3.5 \: \times \: \cancel{3.5}^{ \: \: 0.5} \: }$

$:\implies\sf Area \: of \: circle \: 1 = 22 \times 0.5 \times 3.5$

$:\implies\sf Area \: of \: circle\: 1 = 22 \times 1.75$

$:\implies\sf Area \: of \: circle\: 1 = 38.5$

$\dashrightarrow\:\: \underline{ \boxed{\sf Area = 38.5 \: cm²}}$

Now, For Area of Circle 2 :

${\longrightarrow{\bf{ Radius = 7 cm}}}$

${\longrightarrow{\bf{ \pi = \dfrac{22}{7} }}}$

$\dashrightarrow\:\:\sf Area \: of \: circle \: 2 = \pi r^{2}$

$\dashrightarrow\:\:\sf Area \: of \: circle \: 2 = \dfrac{22}{7} \times (7)^{2}$

$\dashrightarrow\:\:\sf Area \: of \: circle \: 2 = \dfrac{22}{7} \times 7 \times 7$

$\dashrightarrow\:\:\sf Area \: of \: circle \: 2 = \dfrac{22}{7} \times 49$

$\sf \longrightarrow \: Area \: = {\dfrac{22}{ \cancel{7}^{ \: \: 1} } \: \times \: \cancel{49}^{ \: \: 7} \: }$

$\dashrightarrow\:\:\sf Area \: of \: circle \: 2 = 22 \times 7$

$\dashrightarrow\:\:\sf Area \: of \: circle \: 2 = 154$

$\dashrightarrow\:\: \underline{ \boxed{\sf Area = 154 \: cm²}}$

Then, The area between the circle will be -

(Area of circle 2 - Area of circle 1)

$:\implies\sf 154 - 38.5$

$:\implies\sf 115.5$

$\dashrightarrow\:\: \underline{ \boxed{\sf Area = 115. 5 \: cm²}}$

__________________________

Another Method -

By Taking common -

$\underline{\sf Solution :}$

Let's we consider the inner radius be " r " and outer radius be " R " respectively.

So,

↬ πR² - πr²

Taking " π " and common :

→ π(R² - r²)

Substituting the respective values, we get :

$\dashrightarrow\:\:\sf {\dfrac{22}{7} \times {7}^{2} - {3.5}^{2}}$

$\dashrightarrow\:\:\sf {\dfrac{22}{7} \times (49 - 12.25)}$

$\dashrightarrow\:\:\sf {\dfrac{22}{7} \times 36.75 }$

$\sf \longrightarrow \: Area \: = {\dfrac{22}{ \cancel{7}^{ \: \: 1} } \: \times \: \cancel{36.75}^{ \: \: 5.25} \: cm}$

$\dashrightarrow\:\:\sf {22 \times 5.25 }$

$\dashrightarrow\:\:\sf {115.5 }$

$\dashrightarrow\:\: \underline{ \boxed{\sf Area = 115. 5 \: cm²}}$

Answer 2

${\boxed{\underline{\tt{ \orange{Required \: \: answer:-}}}}}$

★GIVEN:-

• Two concentric Circles

• smaller circle radii - 3.5cm

• Larger circle radii - 7cm

★TO FIND :-

• Area between the circle(shaded region)

★FORMULA USED:-

• $\sf{AREA \: = \: \pi \: [ R^2 - r^2]}$
• $\sf{ {a}^{2} - {b}^{2} = (a - b)(a + b)}$

★SOLUTION:-

$: \implies \sf{ \pi \: [ {7}^{2} - {3.5}^{2} ]}$

$: \implies \sf{ \pi \: (7 - 3.5)(7 + 3.5)}$

$: \implies \sf \: {36.75 \pi}$

PUTTING PI VALUE AS 22/7

$: \implies \sf{36.75 \times \frac{22}{7} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \boxed{ \underline{ \purple{115.5 {cm}^{2} }}}}$