Question

if the ratio of the areas of two circles is 16:9 , then the ratio of their radius in the same order as their areas will be
A 16:9
B 9:16
C 4:3
D 3:4​

Answer 1

Step-by-step explanation:

ratio of areas = 16:9

that is π(R1)² : π(R2)² = 16:9

R1 : R2 = 4:3

option c

Answer 2

Given data : The ratio of the areas of two circles is 16:9

To find : The ratio of the radius of the circle.

Solution :

Let, the ratio of the areas of first circle to second be 16:9

{ formula of area of circle = π * r²

Where,

• π = 22/7
• r = radius of circle }

Let, radius of first circle be R and radius of second circle be r .

Hence,

• Formula of area of first circle = π * R²
• Formula of area of second circle = π * r²

Now,

$\bf{\rightarrow{\blue{ \frac{area \: of \: first \: circle}{area \:of \: second \: circle } = \frac{16}{9} }}}$

$\bf{\rightarrow{\blue{\frac{\pi {R}^{2} }{\pi {r}^{2} } = \frac{16}{9} }}}$

$\bf{\rightarrow{\blue{\frac{{R}^{2} }{ {r}^{2} } = \frac{16}{9} }}}$

$\bf{\rightarrow{\blue{ {( \frac{R}{r}) }^{2} = \frac{16}{9} }}}$

$\bf{\rightarrow{\blue{\frac{R}{r} = \sqrt{ \frac{16}{9} } }}}$

$\bf{\rightarrow{\blue{ \frac{R}{r} = \frac{4}{3} }}}$

Answer: Hence, the ratio of the radius of the two circles will be 4:3 .