G10Exercise1.2

November 18, 2021 by editor

i	$\begin{align}\text{Arc Length}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &=14+ \frac{180}{360}\times2\times\frac{22}{7}\times 7 \\[5pt] &=14+22\\[5pt] &=\underline{\underline{36cm}}\\[5pt]\end{align}$
ii	$\begin{align}\text{Arc Length}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &=28+ \frac{90}{360}\times2\times\frac{22}{7}\times 14 \\[5pt] &=28+22\\[5pt] &=\underline{\underline{50cm}}\\[5pt]\end{align}$
iii	$\begin{align}\text{Arc Length}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &=2\times21+ \frac{60}{360}\times2\times\frac{22}{7}\times 21 \\[5pt] &=42+22\\[5pt] &=\underline{\underline{64cm}}\\[5pt]\end{align}$
iv	$\begin{align}\text{Arc Length}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &=2\times7+ \frac{200}{360}\times2\times\frac{22}{7}\times 7 \\[5pt] &=14+\frac{220}{9}\\[5pt] &=14+24\frac{4}{9}\\[5pt] &=\underline{\underline{38\frac{4}{9}cm}}\\[5pt]\end{align}$
i	$\begin{align}\text{Perimeter}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &180=2r+ \frac{180}{360}\times2\times\frac{22}{7}\times r \\[5pt] &7\times180=2r\times7+ \frac{22r}{7}\times7 \\[5pt] &7\times180=14r+22r \\[5pt] &r=\frac{7\times180}{36} \\[5pt] &=\underline{\underline{35cm}}\\[5pt]\end{align}$
ii	$\begin{align}\text{Perimeter}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &43=2r+ \frac{120}{360}\times2\times\frac{22}{7}\times r \\[5pt] &21\times43=2r\times21+ \frac{44r}{21}\times21 \\[5pt] &21\times43=42r+44r \\[5pt] &r=\frac{21\times43}{86} \\[5pt] &=\underline{\underline{10.5cm}}\\[5pt]\end{align}$
i	$\begin{align}\text{Perimeter}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &64=2\times21+ \frac{\theta}{360}\times2\times\frac{22}{7}\times 21 \\[5pt] &64=42+\frac{11\theta}{30}\\[5pt] &\frac{11\theta}{30}=64-42\\[5pt] &\frac{30}{11}\times\frac{11\theta}{30}=22\times\frac{30}{11}\\[5pt] &=\underline{\underline{60^\theta cm}}\\[5pt]\end{align}$
ii	$\begin{align}\text{Perimeter}& =2r+\frac{\theta}{360}\times2\Pi r \\[5pt] &53=2\times21+ \frac{\theta}{360}\times2\times\frac{22}{7}\times 21 \\[5pt] &53=42+\frac{11\theta}{30}\\[5pt] &\frac{11\theta}{30}=53-42\\[5pt] &\frac{11\theta}{30}=11\\[5pt] &\theta=\frac{11\times30}{11}\\[5pt] &=\underline{\underline{30^\theta cm}}\\[5pt]\end{align}$

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November 4, 2021 by admin

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