Question

The sum of the radii of two circles is 286 cm and the area between the concentric circle is 50336 cm² what are the radii (in cm) of the two circles? Take \(\pi =\frac{{22}}{7}\)
1. 171 and 84
2. 91 and 84
3. 115and 91
4. 115 and 171

Answer 1

Correct Answer - Option 4 : 115 and 171

Given:

Sum of radii = 286cm

Area of concentric circles = 50336 cm²

Formula:

Area of circle = πr²

Calculation:

Let area of bigger circle and smaller circle be R cm and r cm respectively.

⇒ πR² - πr² = 50336

⇒ R² - r² = 16016

⇒ (R - r)(R + r) = 16016

⇒ (R - r) = 56

 (R + r) = 286

Solving,

R = 171 cm and r = 115cm

∴ Radius of smaller circle and bigger circle is 115cm and 171cm respectively.