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8.The outfield fencing for a Minor League field forms a circular sector with home plate as thecenter. (See the figure at the top of page 681.) The fence is placed at a uniform distance of2130 ft from home plate. The boundaries of the fence, which extends partway into foulterritory, create an angle of 110 degrees with home plate. At $21 per foot, how much willthe fence cost? (Round to the nearest $10.)

Sagot :

The Solution.

Representing the problem in a diagram, we get

To find the length of the boundaries of the fence, we shall use the formula below:

[tex]\begin{gathered} \text{Length}=\frac{\theta}{360}\times2\pi r \\ \text{Where }\theta=110^o \\ \pi=3.14 \\ r=2130\text{ ft} \end{gathered}[/tex]

Substituting these values in the formula, we get

[tex]\begin{gathered} \text{Length}=\frac{110}{360}\times2\times3.14\times2130 \\ \\ \text{ =}\frac{11\times3.14\times2130}{18}=4087.23\text{ fe}et \end{gathered}[/tex]

We were told that each foot cost $21.

So, the cost of the fence is

[tex]\frac{4087.23}{21}=\text{ \$194.63}\approx\text{ \$190}[/tex]

Therefore, the correct answer is $190

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