When she is on holidays, Barbara sees the building shown on the right - Junior Cycle Mathematics - Question 13 - 2018

First, we need to calculate the actual surface area using the extreme radius values of 8 m and 10 m:

1. For $r = 8 \text{ m}$:

   $S.A. = 4\pi (8)^2 = 4\pi (64) = 256\pi \text{ m}^2$

   The error in estimate is:

   $\text{Error} = 324\pi - 256\pi = 68\pi$

   Now, we find the percentage error:

   $\% \text{Error} = \left( \frac{\text{Error}}{\text{Actual S.A.}} \right) \times 100 = \left( \frac{68\pi}{256\pi} \right) \times 100 = \frac{68}{256} \times 100 \approx 26.5\% \approx 27\%$ (to the nearest percent)

2. For $r = 10 \text{ m}$:

   $S.A. = 4\pi (10)^2 = 4\pi (100) = 400\pi \text{ m}^2$

   The error in estimate is:

   $\text{Error} = 400\pi - 324\pi = 76\pi$

   Now, we find the percentage error:

   $\% \text{Error} = \left( \frac{76\pi}{400\pi} \right) \times 100 = \frac{76}{400} \times 100 = 19\%$

The maximum value of the percentage error is therefore:

$\max(27\%, 19\%) = 27\%$