Question

If the area of a semi-circle protractor is 44/7 sq cm. Find the diameter

Answer 1

$\textbf{Given:}$

$\textsf{Area of the semi-circle protractor is}\;\mathsf{\dfrac{44}{7}\;sq.cm}$

$\textbf{To find:}$

$\textsf{Find the diameter}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\textsf{Area of the semi-circle protractor}\mathsf{=\dfrac{44}{7}\;sq.cm}$

$\implies\mathsf{\dfrac{\pi\,r^2}{2}=\dfrac{44}{7}}$

$\implies\mathsf{\dfrac{1}{2}{\times}\dfrac{22}{7}{\times}r^2=\dfrac{44}{7}}$

$\implies\mathsf{11{\times}r^2=44}$

$\implies\mathsf{r^2=\dfrac{44}{11}}$

$\implies\mathsf{r^2=4}$

$\implies\mathsf{r=2\;cm}$

$\mathsf{Now,}$

$\textsf{Diameter of the semi-circle protractor}$

$\mathsf{=2{\times}Radius}$

$\mathsf{=2{\times}2}$

$\mathsf{=4\;cm}$

$\textbf{Answer:}$

$\mathsf{Diameter\;is\;4\;cm}$

Answer 2

Given:- The area of a semi-circle protractor is 44/7 sq cm.

To find:- The diameter.

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$\sf{\underline{According\: to\: the\: question}}$

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$\sf{\dashrightarrow{\dfrac{\pi r^2}{2} = \dfrac{44}{7}}}$

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$\sf{\dashrightarrow{\dfrac{1}{2} \times \dfrac{22}{7} \times r^2 = \dfrac{44}{7}}}$

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$\sf{\dashrightarrow{11 \times r^2 = 44}}$

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$\sf{\dashrightarrow{r^2 = \dfrac{44}{11}}}$

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$\sf{\dashrightarrow{r^2 = 4}}$

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$\sf{\dashrightarrow{r = 2\: cm}}$

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Now, diameter of the semi-circle protractor.

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$\sf{\dashrightarrow{2 \times r}}$

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$\sf{\dashrightarrow{2 \times 2}}$

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$\mathfrak{\dashrightarrow{\boxed{\pink{4\: cm}}}}$

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Hence,

• The diameter is 4 cm.