1)
Area of largest circle - 2 * Area of one smaller circle = Area of the shaded region

AE = diameter of large circle = 48cm
radius of larger circle = diameter / 2 = 48cm / 2 = 24cm

4 circles fit across the diameter of the circle, so the diameter of the larger circle = 4 * diameter of the smaller circle
diameter of larger circle = 48cm = 4 * diameter of the smaller circle
diameter of the smaller circle = 48cm / 4 = 12cm
radius of smaller circle = diameter / 2 = 12cm / 2 = 6cm

Area of a circle = pi * r^2

Now plug the circle area equation into the first equation:
$A_{shaded}=A_{l} - 2*A_{s}\\\\A_{shaded}=[\pi (r_{l})^{2}]-2*[\pi (r_{s})^{2}]\\\\A_{shaded}=[\pi (48cm)^{2}]-2*[\pi (6cm)^{2}]\\\\A_{shaded}=2304\pi-72\pi\\\\Area\ of\ shaded\ region\ is\ 2232\pi.$

2)
Area of the shaded region = 2/7 * Area of the smaller circle
Area of the unshaded region = Area of larger circle + Area of smaller circle - Area of shaded region * 2
$A_{unshaded}=[\pi (r_{1})^{2}]+[\pi (r_{2})^{2}]-2*[\pi (r_{2})^{2}]*\frac{2}{7}\\\\A_{unshaded}=[\pi (10cm)^{2}]+[\pi (7cm)^{2}] -\frac{4}{7}[\pi (7cm)^{2}]\\\\A_{unshaded}=100\pi\ cm^{2}+49\pi\ cm^{2}-\frac{4*49\pi\ cm^{2}}{7}\\\\A_{unshaded}=149\pi\ cm^{2}-(4*7*\pi\ cm^{2})\\\\A_{unshaded}=149\pi\ cm^{2}-28\pi\ cm^{2}\\\\\\A_{unshaded}=121\pi\ cm^{2}$

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4 years ago