The area (in m2) of a circular path of uniform width x metres surrounding a circular region of diameter d metres is _____.
Answer & explanation
Correct answer: option 2
We know that,
Area of path = π(R2 – r2)
According to the question,
Radius of circular region (r) = d/2
Width of path = x m
External radius of path (R) = d/2 + x
We know that,
Area of path = π(R2 – r2) = π[(d/2 + x)2 – (d/2)2] = π [d2/4 + x2 + dx – d2/4] = π [x2 + dx]
= πx (x + d)