Maths · Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre

The difference between the radii of the smaller circle and the bigger circle is

The difference between the radii of the smaller circle and the bigger circle is \( 7 \mathrm{cm} \) and the difference between the areas of the two circles is 1078 sq \( \mathrm{cm} \) What is the radius of the smaller circle in cm?

  • A. 28
  • B. 21
  • C. 17.5
  • D. 35

Step-by-step solution

Let R be the radius of the bigger circle and r be the radius of the smaller circle. Given R - r = 7 and π(R² - r²) = 1078. Using R² - r² = (R - r)(R + r) = 7(R + r), we get 7π(R + r) = 1078. Taking π = 22/7, then R + r = 1078 / (7 * 22/7) = 1078 / 22 = 49. Solving R + r = 49 and R - r = 7 gives r = (49 - 7)/2 = 21.
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