Resources for Arc Lengths Problems
-
Questions
10
With Worked SolutionClick Here -
Video Tutorials
2
Click Here
Arc Lengths Problems Theory
![\begin{multicols}{2} \textbf{Example 1}\\ Find the perimeter of the shape given that \(A B=4 \text{~cm}\) and \(BC=4 \text{~cm}\)\\ \begin{center} \begin{tikzpicture}[scale=0.7,line width=1pt] \coordinate[label=below:C] (O) at (0,0); \coordinate[label=below:B] (B) at (left:4); \coordinate[label=below:A] (A) at (left:8); \draw (O) arc (0:180:2); \draw (O) arc (0:180:4); \draw (A)--(B) node[below,midway] {4 cm}; \path (O)--(B) node[below,midway] {4 cm}; \end{tikzpicture} \end{center} \textbf{Example 1 solution}\\ \(\begin{aligned} \text{The semicircle on } AC:\; AC&=\frac{180^{\circ}}{360^{\circ}} \times 2 \pi \times 4\\ & =\frac{1}{2} \times 2 \pi \times 4 \\ & =4 \pi \text{ cm} \end{aligned}\)\\ \(\begin{aligned} \text{The semicircle on } B C:\;B C & =\frac{180^{\circ}}{360^{\circ}} \times 2 \pi \times 2 \\ & =\frac{1}{2} \times 2 \pi \times 2 \\ & =2 \pi \text{ cm} \end{aligned}\)\\ \(\begin{aligned} \therefore \text { Perimeter } & =4+4 \pi+2 \pi . \\ & =(4+6 \pi) \text{ cm}. \end{aligned}\) \columnbreak \textbf{Example 2}\\ Find the perimeter of the shape given that \(A C\) has a diameter of \(7 \text{~cm}\) The arc \(A B\) and the are \(B C\) have radii \(2.5 \text{~cm}\) and \(\theta=120^{\circ}\)\\ \begin{center} \begin{tikzpicture}[scale=0.4,line width=1pt] \coordinate[label=below:] (O) at (0,0); \coordinate[label=below:B] (O1) at (0,-2); \coordinate[label=right:C] (C) at (right:7); \coordinate[label=left:A] (A) at (left:7); \coordinate[label=below:E] (E) at (-4.3,-3.5); \coordinate[label=below:F] (F) at (4.5,-3.5); %\draw (E)--(O1) arc (20:140:2.5)--(E); %\draw (F)--(O1)+(right:4.35) arc (20:140:2)--(F); \draw (C) arc (0:180:7); \draw[dashed] (O)--(120:7) node[right,midway] {3.5 cm}; \draw[out=110,in=40,looseness=1] (O1) to (A); \draw[out=70,in=150,looseness=1] (O1) to (C); \draw[dashed] (A)--(E) node[left,midway]{2.5 cm}--(O1); \draw[dashed] (O1)--(F)--(C)node[right,midway]{2.5 cm}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,"\(120^{\circ}\)"] {angle=O1--E--A}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,"\(120^{\circ}\)"] {angle=C--F--O1}; \end{tikzpicture} \end{center} \textbf{Example 2 solution}\\ The semicircle \(A C:\) \; \(\begin{aligned}[t] A C&=\frac{180^{\circ}}{360^{\circ}} \times 2 \pi \times 3.5 \\ & =\frac{1}{2} \times 7 \pi \\ & =3.5 \pi \text{ cm} \end{aligned}\)\\ The arc \(A B:\)\; \(\begin{aligned}[t] AB&=\frac{120^{\circ}}{360^{\circ}} \times 2 \pi \times 2.5\\ & =\frac{1}{3} \times 5 \pi \\ & =\frac{5 \pi}{3} \end{aligned}\)\\ arc \(A B=\) arc \(B C\; \therefore B C=\dfrac{5 \pi}{3}\)\\ \(\begin{aligned} \therefore \text { Perimeter } & =3.5 \pi+\frac{5 \pi}{3}+\frac{5 \pi}{3} \\ & =\left(\frac{7}{2}+\frac{5}{3}+\frac{5}{3}\right) \pi=\frac{41 \pi}{6} \text{~cm} \end{aligned}\) \end{multicols}](/media/qatbadf5/7961.png)
NSW Y8 Maths Area and Perimeter Arc Lengths Problems
Videos
Videos relating to Arc Lengths Problems.
-
Arc Lengths Problems - Video - Arc Lengths Problems 1
You must be logged in to access this resource -
Arc Lengths Problems - Video - Arc Lengths Problems 2
You must be logged in to access this resource
Plans & Pricing
With all subscriptions, you will receive the below benefits and unlock all answers and fully worked solutions.
-
Teachers TutorsFeaturesFreeProAll ContentAll courses, all topicsQuestionsAnswersWorked SolutionsSystemYour own personal portalQuizbuilderClass ResultsStudent ResultsExam RevisionRevision by TopicPractise ExamsAnswersWorked SolutionsAwesome StudentsFeaturesFreeProContentAny course, any topicQuestionsAnswersWorked SolutionsSystemYour own personal portalBasic ResultsAnalyticsStudy RecommendationsExam RevisionRevision by TopicPractise ExamsAnswersWorked Solutions