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The circumference of a circle is 31.4cm. Find the radius and the area of the circle. (Take \[\pi =3.14\]).
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Hint: We know the circumference of a circle is \[2\pi r\]. Find the radius of the circle from the circumference. After finding radius, find the area of a circle using the formula of area.
Complete step-by-step answer:
We know that circumference of a circle is equal to \[2\pi r\], where r is the radius of the circle.
\[\therefore \]Circumference of circle = \[2\pi r\].
We are given the value of circumference of the circle = 31.4cm.
We need to find the radius ‘r’ of the circle.
\[\begin{align}
& \Rightarrow 2\pi r=31.4 \\
& r=\dfrac{31.4}{2\pi }=\dfrac{31.4}{2\times 3.14}=\dfrac{3.14\times 10}{2\times 3.14} \\
& =\dfrac{10}{2}=5cm \\
\end{align}\]
Hence, we got the radius of the circle as 5cm.
Now let us find the area of the circle.
We know the area of a circle is given by \[\pi {{r}^{2}}\].
Area\[=\pi {{r}^{2}}=\pi \times {{5}^{2}}=\pi \times 5\times 5\]
\[=3.14\times 25=78.5c{{m}^{2}}\]
Hence, we got the radius of the circle as 5cm and the area of the circle as \[78.5c{{m}^{2}}\]respectively.
Note: To find the diameter of the circle you can take twice the radius of the circle i.e. diameter \[=2\times \]radius. We can find the area of the circle by directly substituting the value of diameter instead of radius.
radius\[=\dfrac{diameter}{2}\Rightarrow r=\dfrac{d}{2}\], area\[=\pi {{r}^{2}}=\pi \times {{\left( \dfrac{d}{2} \right)}^{2}}\]
area\[=\dfrac{\pi {{d}^{2}}}{4}\]
\[\therefore \] area of circle can be also said as \[\dfrac{\pi {{d}^{2}}}{4}\].
Complete step-by-step answer:
We know that circumference of a circle is equal to \[2\pi r\], where r is the radius of the circle.
\[\therefore \]Circumference of circle = \[2\pi r\].
We are given the value of circumference of the circle = 31.4cm.
We need to find the radius ‘r’ of the circle.
\[\begin{align}
& \Rightarrow 2\pi r=31.4 \\
& r=\dfrac{31.4}{2\pi }=\dfrac{31.4}{2\times 3.14}=\dfrac{3.14\times 10}{2\times 3.14} \\
& =\dfrac{10}{2}=5cm \\
\end{align}\]
Hence, we got the radius of the circle as 5cm.
Now let us find the area of the circle.
We know the area of a circle is given by \[\pi {{r}^{2}}\].
Area\[=\pi {{r}^{2}}=\pi \times {{5}^{2}}=\pi \times 5\times 5\]
\[=3.14\times 25=78.5c{{m}^{2}}\]
Hence, we got the radius of the circle as 5cm and the area of the circle as \[78.5c{{m}^{2}}\]respectively.
Note: To find the diameter of the circle you can take twice the radius of the circle i.e. diameter \[=2\times \]radius. We can find the area of the circle by directly substituting the value of diameter instead of radius.
radius\[=\dfrac{diameter}{2}\Rightarrow r=\dfrac{d}{2}\], area\[=\pi {{r}^{2}}=\pi \times {{\left( \dfrac{d}{2} \right)}^{2}}\]
area\[=\dfrac{\pi {{d}^{2}}}{4}\]
\[\therefore \] area of circle can be also said as \[\dfrac{\pi {{d}^{2}}}{4}\].
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