Question

The radius of a circle is greater than the radius of other circle by 3m . The sum of their areas is 89π m^2 . Find the radius of each circle.

Answer 1

Answer:

radius of smaller circle = 5m

radius of larger circle = 8m

Step-by-step explanation:

Formula:-

Area of circle with radius r is given by,

Area of circle, A = πr²

Let 'r' be the radius of smaller circle, then radius of large circle = r+3

It is given that sum of areas = 89π m^2

To find r

Sum of  areas = πr² + π(r +3)² =  89π m^2

⇒ π[r² + (r +3)²] =  89π

⇒ r² + (r +3)² = 89

⇒ r²  + r² +  6r + 9 = 89

⇒ 2r² +  6r + 9 - 89 = 0

⇒ 2r² +  6r - 80 = 0

⇒ r² +  3r  - 40 = 0 ----(1)

eq(1) is a quadratic equation.

Solving we get

r = 5 and r = -8

we take +ve values, so r = 5

Therefore radius of smaller circle = 5m

And radius of larger circle = r + 3 = 5 = 3 = 8m

Answer 2

Step-by-step explanation:

R1=5

R2=8

SHOUT-OUT TO KING AP