2 years ago

1. Use the Pythagorean Theorem to find then find the perimeter and area of each

Mathematics

1 answer:

Reil [10]2 years ago

6 0

haf ki liksa sa na

hs k

hsvst

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Find (a) arc length and (b) Area of a sector.

barxatty [35]

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a) 29.45 cm (2 dp)

b) 220.89 cm² (2 dp)

Step-by-step explanation:

Formula

$\textsf{Arc length}=r \theta$

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

Calculation

Given:

$\theta=\dfrac{5 \pi}{8}$
r = 15 cm

$\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left(\dfrac{5 \pi}{8}\right)\\& = \dfrac{75}{8} \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}$

$\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(15^2) \left(\dfrac{5 \pi}{8}\right)\\\\& = \dfrac{225}{2}\left(\dfrac{5 \pi}{8}\right)\\\\ & = \dfrac{1125}{16} \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}$

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