Answer:
S = pi^2 * (8^2 - 10^2)
= pi^2 * (-4)
= -12.57 pi^2
The value of S is approximately -12.57 * pi^2. To express this value to three significant figures, we would round it to -13 * pi^2, which is the same as -12.6 * pi^2. So the final answer is -12.6 * pi^2.