The radius of a circle is greater than the radius of othercircle by 3

1.	The radius of a circle is greater than the radius of othercircle by 3 m. The sum of their areas is 89Tt m2. Find theradius of each circie.76
Answer» 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

The radius of a circle is greater than the radius of othercircle by 3 m. The sum of their areas is 89Tt m2. Find theradius of each circie.76

Answer»

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