Question

25. Find the area of ring between two concentric circles whose circumferences are
75 m & 55m.​

Answer 1

${\large{\frak{\pmb{\underline{Let's \; understand \; the \; question}}}}}$

★ Find the area of ring between two concentric circles whose circumferences are 75 m & 55m.

★ We have to find out the area of the rings between two concentric circles. Their circumference are given as 75 metres and 55 metres. It is already cleared that there are two circles i.e., one big or small respectively. Let's see what to do.

${\large{\frak{\pmb{\underline{Given \; that}}}}}$

★ Circumference of concentric circles = 75 metres and 55 metres.

Henceforth, let

• 75 metres is the circumference of big concentric circle.

• 55 metres is the circumference of small concentric circle.

${\large{\frak{\pmb{\underline{To \; find}}}}}$

★ The area of ring between two concentric circles.

${\large{\frak{\pmb{\underline{Solution}}}}}$

★ The area of ring between two concentric circles = 207.243454 metres²

${\large{\frak{\pmb{\underline{Using \; formulas}}}}}$

★ Formula to find circumference of circle.

★ Formula to find area of circle.

${\large{\frak{\pmb{\underline{Using \; formulas}}}}}$

★ Circumference of circle = 2πr

★ Area of circle = πr²

${\large{\frak{\pmb{\underline{Where,}}}}}$

★ π is pronounced as pi

★ The value of π is 22/7 or 3.14

★ r dentoes radius

★ ² denotes square

${\large{\frak{\pmb{\underline{Full \; Solution}}}}}$

~ As we already understand that what the question says! Now let's see how to solve this question. Firstly we have to find the radius of both circles by using formula to find circumference of circle. Let's do it!

☀ Finding radius of big circle first.!

$\sf \rightarrow Circumference \: of \: big \: circle = 75 \: m \\ \\ \sf \longrightarrow \: Henceforth \\ \\ \sf :\implies \: 2\pi r = 75 \\ \\ \sf :\implies 2(3.14)(r) = 75 \\ \\ \sf :\implies 2 \times 3.14 \times r = 75 \\ \\ \sf :\implies 6.28 \times r = 75 \\ \\ \sf :\implies r = 75 \div 6.28 \\ \\ \sf :\implies r = 11.94 \: m \\ \\ \sf :\implies Radius = 11.94 \: metres$

☀ Finding radius of small circle now.!

$\sf \rightarrow Circumference \: of \: small \: circle = 55 \: m \\ \\ \sf \longrightarrow \: Henceforth \\ \\ \sf :\implies \: 2\pi r = 55 \\ \\ \sf :\implies 2(3.14)(r) = 55 \\ \\ \sf :\implies 2 \times 3.14 \times r = 55 \\ \\ \sf :\implies 6.28 \times r = 55 \\ \\ \sf :\implies r = 55 \div 6.28 \\ \\ \sf :\implies r = 8.75 \: m \\ \\ \sf :\implies Radius = 8.75 \: metres$

Henceforth, we get radius as

➟ Radius of big circle = 11.94 m

➟ Radius of small circle = 8.75 m

~ Now bt using formula to find area of circle let's find area of ring between two concentric circles. Note : We have to use formula properly and according to the question. Let's do it!

☀ Finding area of ring.!

$\sf \rightarrow Area \: of \: circle = Area \: of \: big \: circle - \: Area \: of \: small \: circle \\ \\ \sf \longrightarrow \: Henceforth \\ \\ \sf :\implies \: \pi R^{2} - \pi r^{2} \\ \\ \sf :\implies \pi (R^{2}-r^{2} \\ \\ \sf :\implies 3.14(11.94^{2} - 8.75^{2}) \\ \\ \sf :\implies 3.14(142.5636-76.5625) \\ \\ \sf :\implies 3.14(66.0011) \\ \\ \sf :\implies 3.14 \times 66.0011 \\ \\ \sf :\implies 3.14 \times 66.0011 \\ \\ \sf :\implies 207.243454 \: m^{2}$

Henceforth, we get area as

➟ Area of ring between two concentric circles = 207.243454 m²

Answer 2

Answer:

Let

′

sunderstandthequestion

★ Find the area of ring between two concentric circles whose circumferences are 75 m & 55m.

★ We have to find out the area of the rings between two concentric circles. Their circumference are given as 75 metres and 55 metres. It is already cleared that there are two circles i.e., one big or small respectively. Let's see what to do.

{\large{\frak{\pmb{\underline{Given \; that}}}}}

Giventhat

Giventhat

★ Circumference of concentric circles = 75 metres and 55 metres.

Henceforth, let

75 metres is the circumference of big concentric circle.

55 metres is the circumference of small concentric circle.

{\large{\frak{\pmb{\underline{To \; find}}}}}

Tofind

Tofind

★ The area of ring between two concentric circles.

{\large{\frak{\pmb{\underline{Solution}}}}}

Solution

Solution

★ The area of ring between two concentric circles = 207.243454 metres²

{\large{\frak{\pmb{\underline{Using \; formulas}}}}}

Usingformulas

Usingformulas

★ Formula to find circumference of circle.

★ Formula to find area of circle.

{\large{\frak{\pmb{\underline{Using \; formulas}}}}}

Usingformulas

Usingformulas

★ Circumference of circle = 2πr

★ Area of circle = πr²

{\large{\frak{\pmb{\underline{Where,}}}}}

Where,

Where,

★ π is pronounced as pi

★ The value of π is 22/7 or 3.14

★ r dentoes radius

★ ² denotes square

{\large{\frak{\pmb{\underline{Full \; Solution}}}}}

FullSolution

FullSolution

~ As we already understand that what the question says! Now let's see how to solve this question. Firstly we have to find the radius of both circles by using formula to find circumference of circle. Let's do it!

☀ Finding radius of big circle first.!

\begin{gathered} \sf \rightarrow Circumference \: of \: big \: circle = 75 \: m \\ \\ \sf \longrightarrow \: Henceforth \\ \\ \sf :\implies \: 2\pi r = 75 \\ \\ \sf :\implies 2(3.14)(r) = 75 \\ \\ \sf :\implies 2 \times 3.14 \times r = 75 \\ \\ \sf :\implies 6.28 \times r = 75 \\ \\ \sf :\implies r = 75 \div 6.28 \\ \\ \sf :\implies r = 11.94 \: m \\ \\ \sf :\implies Radius = 11.94 \: metres\end{gathered}

→Circumferenceofbigcircle=75m

⟶Henceforth

:⟹2πr=75

:⟹2(3.14)(r)=75

:⟹2×3.14×r=75

:⟹6.28×r=75

:⟹r=75÷6.28

:⟹r=11.94m

:⟹Radius=11.94metres

☀ Finding radius of small circle now.!

\begin{gathered}\sf \rightarrow Circumference \: of \: small \: circle = 55 \: m \\ \\ \sf \longrightarrow \: Henceforth \\ \\ \sf :\implies \: 2\pi r = 55 \\ \\ \sf :\implies 2(3.14)(r) = 55 \\ \\ \sf :\implies 2 \times 3.14 \times r = 55 \\ \\ \sf :\implies 6.28 \times r = 55 \\ \\ \sf :\implies r = 55 \div 6.28 \\ \\ \sf :\implies r = 8.75 \: m \\ \\ \sf :\implies Radius = 8.75 \: metres\end{gathered}

→Circumferenceofsmallcircle=55m

⟶Henceforth

:⟹2πr=55

:⟹2(3.14)(r)=55

:⟹2×3.14×r=55

:⟹6.28×r=55

:⟹r=55÷6.28

:⟹r=8.75m

:⟹Radius=8.75metres

Henceforth, we get radius as

➟ Radius of big circle = 11.94 m

➟ Radius of small circle = 8.75 m

~ Now bt using formula to find area of circle let's find area of ring between two concentric circles. Note : We have to use formula properly and according to the question. Let's do it!

☀ Finding area of ring.!

\begin{gathered}\sf \rightarrow Area \: of \: circle = Area \: of \: big \: circle - \: Area \: of \: small \: circle \\ \\ \sf \longrightarrow \: Henceforth \\ \\ \sf :\implies \: \pi R^{2} - \pi r^{2} \\ \\ \sf :\implies \pi (R^{2}-r^{2} \\ \\ \sf :\implies 3.14(11.94^{2} - 8.75^{2}) \\ \\ \sf :\implies 3.14(142.5636-76.5625) \\ \\ \sf :\implies 3.14(66.0011) \\ \\ \sf :\implies 3.14 \times 66.0011 \\ \\ \sf :\implies 3.14 \times 66.0011 \\ \\ \sf :\implies 207.243454 \: m^{2}\end{gathered}

→Areaofcircle=Areaofbigcircle−Areaofsmallcircle

⟶Henceforth

:⟹πR

2

−πr

2

:⟹π(R

2

−r

2

:⟹3.14(11.94

2

−8.75

2

)

:⟹3.14(142.5636−76.5625)

:⟹3.14(66.0011)

:⟹3.14×66.0011

:⟹3.14×66.0011

:⟹207.243454m

2

Henceforth, we get area as

➟ Area of ring between two concentric circles = 207.243454 m²