A rubber band is stretched around the four circles (each with radius r cm).

Question

i) Show that the total length of the rubber band is given by the expression r(8+2π)cm.

ii) Show that the area of the shape is given by the expression r^2(12+π) cm^2

Answer 1

Consider two of the circles. The rubber band stretches between two parallel radii, separated by a distance of 2r.

In addition, it stretches 1/4 of the war around a circle. That distance is π/2 r.

Since there are 4 circles, the total length is 4(2r + π/2 r) = r(8+2π)

Use similar reasoning to get the area of the square minus the 4 corners.

Answer 2

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