Multiple choice

The area of a ring is $40\pi \ \text{ cm }^{ 2 }$. If the width of the ring is $4$ cm, then the sum of the radii of circles

  1. $4$
  2. $5$
  3. $3$
  4. $10$
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D Correct answer
Explanation

For an annulus, area = pi(R^2 - r^2) = pi(R - r)(R + r). The width gives R - r = 4, so 4(R + r) = 40 and R + r = 10.

AI explanation

The area of the ring is found by subtracting the area of the inner circle from the area of the outer circle, giving the formula pi * (R^2 - r^2). The width of the ring is the difference between the outer and inner radii (R - r = 4), so we can rewrite R^2 - r^2 as (R - r)(R + r), which simplifies to 4 * (R + r). Setting pi * 4 * (R + r) equal to the given area of 40*pi, we find that 4 * (R + r) = 40, resulting in a sum of radii (R + r) of 10.

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