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: [latex]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}=2304pi-72pi\\Area of shaded region is 2232pi.[/latex] 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 [latex]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}=100pi cm^{2}+49pi cm^{2}-frac{4*49pi cm^{2}}{7}\\A_{unshaded}=149pi cm^{2}-(4*7*pi cm^{2})\\A_{unshaded}=149pi cm^{2}-28pi cm^{2}\\\A_{unshaded}=121pi cm^{2}[/latex]

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2016-09-19 01:02:45

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