Question

Find the area enclosed between two concentric circles of radii 6.3cm and 8.4cm. A third concentric circle is drawn outside the 8.4cm circle. So that the area enclosed between it and the 8.4cm circle is the same as that between the two inner circles. Find the radii of the third circle correct to two decimal places.

Answer 1

Area of the ring between two concentric circles = π(R² - r²)
Where R and r are the radii of the outer and the inner circle respectively
Here there are three concentric circles,
the innermost of radius 6.3cm, the second of radius 8.4cm and the outermost of radius x cm (say)
⇒ π(8.4² - 6.3²) = π(x² - 8.4²)
⇒ π(2 x 8.4² - 6.3²) = πx²
⇒ (2 x 8.4² - 6.3²) = πx²
⇒ (2 x 8.4² - 6.3²) = x²
⇒ (141.12cm² - 39.69cm²) = x²
⇒ x² = 101.43cm²
⇒ x = 10.07cm.