Question

the sum of radii of 2 concentric ciecles is 8cm and difference of their area is 16π cm^2 . find the linear equation for the above statement. and find the radii if the concentric circles graphically.​

Answer 1

Answer:

The radius of outer circle is 5 cm , Area of outer circle is 25 π cm²

The radius of outer circle is 3 cm , Area of outer circle is 9 π cm²

Step-by-step explanation:

Given as :

Two concentric circles with radius R and r

The radius of outer circle = R cm

The radius of inner circle = r cm

The sum of radius = 8 cm

The difference between their area = 16 π cm²

According to question

∵ The sum of radius = 8 cm

So, R + r = 8 cm         ........A

And

The difference between their area = 16 π cm²

∵ Area of circle =  π ( Radius )²

So, π R² - π r² =  16 π cm²

or,  R² -  r² = $\dfrac{16\pi }{\pi }$

Or, ( R + r ) ( R - r ) = 16

From eq A

8 ×  ( R - r ) = 16

Or, R - r = $\dfrac{16}{8}$

i.e R - r = 2                .......B

Solvinf eq A  and eq B

( R + r ) + ( R - r ) = 8 + 2

Or, ( R + R ) + (r - r) = 10

Or, 2 R + 0 = 10

∴   R = $\dfrac{10}{2}$

i.e R = 5 cm

So, The radius of outer circle = R = 5 cm

Area of outer circle = π (5)²  = 25 π cm²

Again

Put the value of R into eq B

R  - r = 2

Or, 5 - r = 2

Or, r = 5 - 2 = 3 cm

So, The radius of inner circle = r = 3 cm

Area of inner circle = π (3)²  = 5 π  cm²

Hence, The radius of outer circle is 5 cm , Area of outer circle is 25 π cm²

And The radius of outer circle is 3 cm , Area of outer circle is 9 π cm² Answer