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Maths Help (1 Viewer)

Thread starter Farhanthestudent005
Start date May 28, 2021

Farhanthestudent005

Member

#1

Find the exact value of the radius r and angle Θ of the sector that has an area of 100cm2 and arc length of 20cm.

Please help me thanks!!!!

C

cossine

Well-Known Member

#2

@Farhanthestudent005

If you know what the the theorem are for arc length and area of sector in radians, you solve be able to solve the question.

jimmysmith560

Le Phénix Trilingue

Moderator

#3

You may want to check out this video. I believe it may help:

C

CM_Tutor

Moderator

Moderator

#4

$\begin{align*} l = r\theta &= 20 \qquad \text{. . . . . . . . . . (2)} \\ A = \cfrac{1}{2}r^2\theta &= 100 \qquad \text{. . . . . . . . . . (2)} \\ \\ \text{Using (2):} \quad r \times r\theta &= 200 \\ r \times 20 &= 200 \quad \text{putting (1) into the equation} \\ r &= 10 \text{ cm} \\ \\ \text{So,} \quad \theta &= \cfrac{20}{r} \\ &= \cfrac{20}{10} \\ &= 2 \text{ radians} \end{align*}$

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