Geometry

Question Analysis

The main focus is using the formula for the area of a ring to solve for the inner radius. Given the area of the ring and the outer radius, we need to apply the formula and perform algebraic operations to find the value of the inner radius.

 

Key Concept Explanation

The area of a ring is calculated by the formula , where  is the area of the ring,  is the outer radius, and  is the inner radius. This formula comes from subtracting the area of the inner circle () from the area of the outer circle ().

 

Step - by - Step Solution

1. Start with the area formula for a ring: .

Substitute  and  into the formula: .

Divide both sides of the equation by  to simplify: