Question

the junior class is building a float for the homecoming parade. part of the float a large, circular - shaped disc with equally sized sectors that are alternately gold and black - the schools colors. the disc has a radius of 8 feet. both sides of the disc must be painted. approximately how many square feet of the disc must be covered with gold paint? 3 of 5 questio 201ft² 402ft² 67ft² 50ft²

Explanation:

Step1: Calculate the area of the circle

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 8\) feet, then \(A=\pi\times8^{2}=64\pi\) square feet.

Step2: Determine the proportion of the gold - painted area

Since the sectors are alternately gold and black, half of each side is gold. And there are two sides. So the proportion of the gold - painted area is \(1\) (because \(\frac{1}{2}\times2 = 1\) of the total area of the disc).

Step3: Calculate the gold - painted area

Substitute \(\pi\approx3.14\) into \(A = 64\pi\). Then \(A\approx64\times3.14=200.96\approx201\) square feet.

Answer:

\(201\mathrm{ft}^{2}\)