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Viefleur [7K]
3 years ago
8

Find (a) the arc length and (b) the area of a sector.

Mathematics
1 answer:
Brut [27]3 years ago
6 0

Answer:

a) 23.56 ft (2 dp)

b) 58.90 ft² (2 dp)

Step-by-step explanation:

<u>Formula</u>

\textsf{Arc length}=r \theta

\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta

\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}

<u>Calculation</u>

Given:

  • \theta=\dfrac{3 \pi}{2}
  • r = 5 ft

\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 5\left(\dfrac{3 \pi}{2}\right)\\& = \dfrac{15}{2} \pi \\& = 23.56\: \sf ft\:(2\:dp)\end{aligned}

\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(5^2) \left(\dfrac{3 \pi}{2}\right)\\\\& = \dfrac{25}{2}\left(\dfrac{3 \pi}{2}\right)\\\\ & = \dfrac{75}{4} \pi \\\\& = 58.90 \: \sf ft^2\:(2\:dp)\end{aligned}

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