Question

The sum of the circumference of two circles is 38π cm and the sum of their areas is 193π cm². Calculate the radii of the circles.​

Answer 1

Answer:

The radii of the circles are 12 cm and 7cm.

Step-by-step explanation:

Let the radii of the circles be $r_{1}\ and\ r_{2}$

Given:

Sum of circumference of two circles= 38π cm

Formula for circumference of a circle with radius r = 2πr

$2\pi r_{1}+2\pi r_{2}=38\pi \\r_{1}+r_{2}=19$------------1

Sum of areas of two circles= 193π cm²

Area of circle with radius r = πr²

$\pi r_{1}^{2}+\pi r_{2}^{2}=193\pi \\r_{1}^{2}+r_{2}^{2}=193$-------2

Substituting r2 = 19 - r1 in equation 2 we get:

$r_{1}^{2}+(19-r_{1})^{2}=193\\2r_{1}^{2}-38r_{1}+168=0\\r_{1}^{2}-19r_{1}+84=0\\(r_{1}-12)(r_{1}-7)=0\\r_{1}=12\ or\ 7$

Then r2 = 19 - r1

$r_{2}=12\ or\ 7$