Question

a miniature golf green is shaped as in the figure. each curve is a semi - circle. determine the area of the green in square metres. round your answer to 1 decimal place. (1 foot = 0.3048 m) a) 11.7 m² b) 5.8 m² c) 62.8 m² d) 6.4 m²

Explanation:

Step1: Analyze the figure's composition

The figure can be seen as a large semi - circle with diameter 12 ft and two small semi - circles with diameter 4 ft. The area of the figure is the area of the large semi - circle minus the area of the two small semi - circles.

Step2: Calculate the radius of the large semi - circle

The diameter of the large semi - circle \(d_1 = 12\) ft, so the radius \(r_1=\frac{12}{2}=6\) ft. The area of a full - circle is \(A=\pi r^{2}\), and the area of the large semi - circle \(A_1=\frac{1}{2}\pi r_1^{2}=\frac{1}{2}\pi(6)^{2}=18\pi\) square feet.

Step3: Calculate the radius of the small semi - circles

The diameter of each small semi - circle \(d_2 = 4\) ft, so the radius \(r_2=\frac{4}{2}=2\) ft. The area of one small semi - circle is \(A_{s}=\frac{1}{2}\pi r_2^{2}=\frac{1}{2}\pi(2)^{2}=2\pi\) square feet. The area of two small semi - circles is equivalent to the area of one full - circle with radius \(r_2\), so \(A_2=\pi r_2^{2}=\pi(2)^{2}=4\pi\) square feet.

Step4: Calculate the area of the figure in square feet

The area of the figure in square feet \(A = A_1 - A_2=18\pi-4\pi = 14\pi\) square feet.

Step5: Convert from square feet to square meters

We know that \(1\) foot \(=0.3048\) m, so \(1\) square foot \(=(0.3048)^{2}\) square meters.
\(A = 14\pi\) square feet. First, \(14\pi\approx14\times3.14 = 43.96\) square feet.
To convert to square meters, we multiply by \((0.3048)^{2}\).
\(A=43.96\times(0.3048)^{2}\)
\(A = 43.96\times0.09290304\)
\(A\approx4.08\approx4.1\) square meters (rounded to 1 decimal place)

Answer:

None of the given options are correct. The correct area, rounded to 1 decimal place, is approximately \(4.1\) \(m^{2}\)