Question

16:26
Q7 The circumferences of two circles are in the ratio 3:4, and then the ratio of their areas will be:
a.
9:16
13:4
C. 6.8
plz help​

Answer 1

$\Large\underline{\underline{\bf \red{Correct\: Question}:}}$

The circumferences of two circles are in the ratio 3:4, and then the ratio of their areas will be:

$\Large\underline{\underline{\sf Given:}}$

• Ratio of Circumference of two circle $\sf{(C_1:C_2)}$=3:4

$\Large\underline{\underline{\sf To\:Find:}}$

• Ratio of area of circles $\sf{(A_1:A_2)}$

$\Large\underline{\underline{\sf Formula \: Used:}}$

${\boxed{\boxed{\sf \pink{Circumference\:of\:Circle(C)=2πr}}}}$

${\boxed{\boxed{\sf \pink{Area\:Of\:Circle(A)=πr^2}}}}$

$\Large\underline{\underline{\sf Solution:}}$

$\implies{\sf \dfrac{C_1}{C_2}=\dfrac{3}{4} }$

$\implies{\sf C_1=2πr_1 }$

$\implies{\sf r_1=\dfrac{3}{2π} }$

$\implies{\sf C_2=2πr_2}$

$\implies{\sf \dfrac{4}{2π}=r_2 }$

$\implies{\sf r_2=\dfrac{2}{π} }$

Area of Circle (A) = πr²

$\implies{\sf A_1=π\left(\dfrac{3}{2π}\right)^2}$

$\implies{\sf A_1=\dfrac{9}{4π^2}×π }$

$\implies{\sf A_1=\dfrac{9}{4π}}$

$\implies{\sf A_2=π \left(\dfrac{2}{π}\right)^2 }$

$\implies{\sf A_2=\dfrac{4}{π}×π }$

$\implies{\sf A_2=\dfrac{4}{π} }$

Ratio of Areas :

$\implies{\sf \dfrac{A_1}{A_2}=\dfrac{\dfrac{9}{4π}}{\dfrac{4}{π}}}$

$\implies{\sf \dfrac{A_1}{A_2}=\dfrac{9}{16} }$

$\Large\underline{\underline{\sf Answer:}}$

Option (a) 9:16

⛬ Ratio of Areas is $\bf{\dfrac{A_1}{A_2}=\dfrac{9}{16}}$

Answer 2

Answer:

$\huge\mathcal\pink{♡Añswer♡}$

Given:

Ratio of Circumference of two circle $\sf{(C_1:C_2)}$

$\Large\underline{\underline{\sf To\:Find:}}$

Ratio of area of circles$\sf{(A_1:A_2)}$

$\Large\underline{\underline{\sf Formula \: Used:}}$

${\boxed{\boxed{\sf \pink{Circumference\:of\:Circle(C)=2πr}}}}$

${\boxed{\boxed{\sf \pink{Area\:Of\:Circle(A)=πr^2}}}}$

$\Large\underline{\underline{\sf Solution:}}$

$\implies{\sf \dfrac{C_1}{C_2}=\dfrac{3}{4}}$⟹

$\implies{\sf C_1=2πr_1}$⟹

$\implies{\sf r_1=\dfrac{3}{2π}}$⟹

$\implies{\sf C_2=2πr_2}$⟹

$\implies{\sf \dfrac{4}{2π}=r_2 }$⟹

$\implies{\sf r_2=\dfrac{2}{π}}$⟹

Area of Circle (A) = πr²

$\implies{\sf A_1=π\left(\dfrac{3}{2π}\right)^2}$⟹

$\implies{\sf A_1=\dfrac{9}{4π^2}×π }$⟹

$\implies{\sf A_1=\dfrac{9}{4π}}$⟹

$\implies{\sf A_2=π \left(\dfrac{2}{π}\right)^2}$⟹

$\implies{\sf A_2=\dfrac{4}{π}×π}$⟹

$\implies{\sf A_2=\dfrac{4}{π}}$⟹

Ratio of Areas :

$\implies{\sf \dfrac{A_1}{A_2}=\dfrac{\dfrac{9}{4π}}{\dfrac{4}{π}}}$⟹

$\implies{\sf \dfrac{A_1}{A_2}=\dfrac{9}{16} }$⟹

$\Large\underline{\underline{\sf Answer:}}$

Option (a) 9:16

Ratio of Areas is$\bf{\dfrac{A_1}{A_2}=\dfrac{9}{16}}$

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