Question

the library of a contemporary elementary school is circular. the floor plan includes sectors reserved for science materials, literary materials, reference materials, and so on. find the area of the reference section excluding its storage area.
the area of the reference section excluding its storage area is □ft².
(round to the nearest hundredth as needed.)

Explanation:

Step1: Find the area of the whole circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius. Given the diameter \(d = 68\) ft, so the radius \(r=\frac{d}{2}=\frac{68}{2}=34\) ft.
The area of the whole circle \(A_{total}=\pi\times34^{2}=\pi\times1156 = 1156\pi\)

Step2: Find the area of the reference - section sector

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector. Here \(\theta = 54^{\circ}\) and \(r = 34\) ft.
The area of the reference - section sector \(A_{ref - sector}=\frac{54}{360}\times\pi\times34^{2}=\frac{54}{360}\times1156\pi=\frac{3}{20}\times1156\pi = 173.4\pi\)

Step3: Find the area of the storage - area circle

The radius of the storage - area circle \(r_{storage}=18\) ft. The area of the storage - area circle \(A_{storage}=\pi\times18^{2}=\pi\times324 = 324\pi\)

Step4: Calculate the area of the reference section excluding its storage area

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Substitute \(\pi\approx3.14\)
\(A = 658.6\times3.14=2068.004\approx2068.00\)

Answer:

\(2068.00\)