A circular embankment is constructed with a radius of 40 meters. A second concentric circular embankment is built around the first, with a width of 12 meters. What is the approximate area of the region between the two embankments?
3470 m2
The first embankment has radius \(r = 40\) m. The second is concentric and 12 m wide, so its radius is \(R = 40 + 12 = 52\) m.
The region between the two circles is an annulus (a ring), whose area is the outer circle's area minus the inner circle's area: \(\pi R^2 - \pi r^2 = \pi(R^2 - r^2)\).
Compute the squares: \(R^2 = 52^2 = 2704\) and \(r^2 = 40^2 = 1600\).
Their difference is \(2704 - 1600 = 1104\), so the area is \(1104\pi\) m\(^2\).
Take \(\pi \approx 3.1416\): \(1104 \times 3.1416 \approx 3468.4\) m\(^2\).
Rounding to the nearest listed value gives about 3470 m\(^2\).
Using the annulus formula \(\pi(R^2 - r^2)\), the approximate area of the region is 3470 m2.
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