Question

${\small{\red{mathcal{\blue{\underline{Question\:For\:Maths\:Experts}}}}}}$

It is given that there are 100 concentric circles i.e. have same centre O.
The radius of 10th circle is 20 cm and the radius of 5th circle is 10 cm. Then find the area of largets (100th) circle.

[Answer :- 125600 cm²]

[Use $\pi$ = 3.14]

Need explanation correct answer will be marked as BRAINLIEST.
​

Answer 1

$\large\bf\underline \blue{Given:-}$

• Radius of 10th circle = 20cm
• Radius of 5th circle = 10cm

$\large\bf\underline \blue{To \: find:-}$

• Area of 100th circle.

$\huge\bf\underline \green{Solution:-}$

$\rm\:It\: is\: given \:that,$

• Radius of 10th circle = 20cm
• and , 5th circle = 10cm

So,

Radius of 1st circle = 2cm

Radius of 2nd circle = 2+2 = 4cm

Radius of 3rd circle = 4+2 = 6cm

So,

radius of circles form an AP as:- 2, 4,6....

we know that,

$\: \: \: \: \: \: \: \: \: \: \: \: \bf\: \pink{a_n = a + (n - 1)d}$

• First term (a) = 2
• common difference (d) = 2

$\longmapsto\rm\:a_n=2 + (100 - 1)2 \\ \\ \longmapsto\rm\:a_n=2 + 99 \times 2 \\ \\ \longmapsto\rm\:a_n=2 + 198 \\ \\ \longmapsto\bf\:a_n=200cm$

So, Radius of 100th circle = 200cm

Now,

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

$\longmapsto\rm\: 3.14 \times {200}^{2} \\ \\\longmapsto\rm\: 3.14 \times 40000 \\ \\ \longmapsto\rm\: 125600 \\ \\ \longmapsto\bf\:125600c{m}^{2}\:\:$

Area of 100th circle = 125600cm²

Answer 2

${\small{\boxed{\overline{\mid{\purple{Given:-}}}}}}$

》Radius of 10th circle = 20cm

》Radius of 5th circle = 10cm

${\small{\boxed{\overline{\mid{\purple{To\:Find}}}}}}$

》Area of 100th circle

${\small{\boxed{\overline{\mid{\purple{Solution:-}}}}}}$

》Radius of the 10th circle =20cm

》and , 5th circle = 10cm

So,

》Radius of 1st circle = 2cm

》Radius of 2nd circle = 2+2 = 4cm

》Radius of 3rd circle = 4+2 = 6cm

So,

》radius of circles form an AP as:- 2, 4,6....

》we know that,

$\small\sf\purple{a_n =a+(n-1)d}$

First term (a) = 2

》common difference (d) = 2

⟼an=2+(100−1)2

⟼an=2+99×2

⟼an=2+198

⟼an=200cm

》So, Radius of 100th circle = 200cm

Now,

》$\small\sf\purple{Area\: of\:circle\: = πr\:}$

⟼3.14×2002

⟼3.14×40000

⟼125600

⟼125600cm2

Area of 100th circle = 125600cm²

${\huge{\boxed{\overline{\mid{\purple{125600cm}}}}}}$