Composite Figures, SM-Bank 022

The diagram below shows the design for a chicken pen at Gayle's farm.

Gayle wishes to construct a fence around the pen. Calculate the amount of fencing required, correct to the next metre. (2 marks)

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Gayle has chosen fencing that costs $22 per metre, with an additional cost of $240 for the installation of a gate. Calculate the total cost of fencing the pen. (2 marks)

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Show Answers Only

a. \(17\ \text{m (next metre)}\)

b. \($614\)

Show Worked Solution

a.	\(\text{Perimeter}\)	\(=2\ \text{radii}+\dfrac{1}{4}\ \text{circumference}\)
		\(=2\times 4.5+\Bigg(\dfrac{1}{4}\times 2\pi r\Bigg)\)
		\(=9+\Bigg(\dfrac{1}{4}\times 2\pi \times 4.5\Bigg)\)
		\(=9 +\dfrac{1}{2}\times 4.5\pi\)
		\(=16.068\dots\)
		\(\approx 17\ \text{m (next metre)}\)

b.	\(\text{Total cost}\)	\(=$22\times 17 +$240\)
		\(=$614\)