To find the area of the painted section between the two circles, we first need to calculate the areas of the outer circle and the inner circle, and then subtract the area of the inner circle from the area of the outer circle.
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Calculate the radius of the outer circle: \[ \text{Diameter} = 10 \text{ ft} \implies \text{Radius} = \frac{10}{2} = 5 \text{ ft} \]
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Calculate the radius of the inner circle: \[ \text{Diameter} = 7 \text{ ft} \implies \text{Radius} = \frac{7}{2} = 3.5 \text{ ft} \]
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Calculate the area of the outer circle: \[ \text{Area} = \pi \times \text{Radius}^2 = \pi \times (5)^2 = 25\pi \text{ square feet} \]
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Calculate the area of the inner circle: \[ \text{Area} = \pi \times \text{Radius}^2 = \pi \times (3.5)^2 = 12.25\pi \text{ square feet} \]
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Calculate the painted area (area between the circles): \[ \text{Painted Area} = \text{Area of Outer Circle} - \text{Area of Inner Circle} \] \[ \text{Painted Area} = 25\pi - 12.25\pi = (25 - 12.25)\pi = 12.75\pi \text{ square feet} \]
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Calculate the numerical value of the painted area (using \(\pi \approx 3.14159\)): \[ \text{Painted Area} \approx 12.75 \times 3.14159 \approx 40.026 \]
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Round to the nearest hundredth: \[ \text{Painted Area} \approx 40.03 \text{ square feet} \]
Thus, the area of the painted section is approximately 40.03 square feet.