Subjects geometry

Ring Area Ff8457

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1. **State the problem:** We need to find the area of a ring-shaped region (annulus) with an inner radius of 15 ft and a width of 5 ft. 2. **Identify the radii:** The inner radius $r_i = 15$ ft. The width of the ring is 5 ft, so the outer radius $r_o = 15 + 5 = 20$ ft. 3. **Formula for the area of an annulus:** $$\text{Area} = \pi (r_o^2 - r_i^2)$$ This formula subtracts the area of the inner circle from the area of the outer circle. 4. **Substitute the values:** $$\text{Area} = 3.14 \times (20^2 - 15^2)$$ 5. **Calculate the squares:** $$20^2 = 400, \quad 15^2 = 225$$ 6. **Subtract the squares:** $$400 - 225 = 175$$ 7. **Calculate the area:** $$\text{Area} = 3.14 \times 175$$ 8. **Multiply:** $$\text{Area} = 549.5$$ **Final answer:** The area of the shaded ring is $549.5$ ft$^2$.