A circular garden having a diameter of 10 m is surrounded by a concrete path that is 1 m wide. Calculate the percentage increase in area resulting from the addition of the path.
44%
Step 1 – Original radius and area:
Diameter = 10 m, so radius \(r_{1} = 5 \text{ m}\) and original area \(A_{1} = \pi r_{1}^{2} = 25\pi\).
Step 2 – New radius (garden + path) and area:
\(r_{2} = 5 + 1 = 6 \text{ m}, \quad A_{2} = \pi r_{2}^{2} = 36\pi\)
Step 3 – Percentage increase in total area:
\(\% \text{ increase} = \dfrac{A_{2} - A_{1}}{A_{1}} \times 100 = \dfrac{36\pi - 25\pi}{25\pi} \times 100\)
\(= \dfrac{11}{25} \times 100 = 44\%\)
Hence the percentage increase is 44%.
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