What is the area of a circle $10$ inches in diameter?

Answer

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Hint: For finding the area of the circle of the given dimension we need to use the formula for the area of a circle which is given by $A=\pi {{r}^{2}}$, where r is equal to the area of the circle. In the above question, we have been given the value of the diameter of the circle to be equal to $10$ inches. The radius of a circle is equal to half of its diameter. Therefore, the radius of the circle will be equal to $5$inches. On finally substituting this value of the radius into the formula for the area of a circle, we will get the final answer.

Complete step by step answer:

We know that the area of a circle is given by the formula

$\Rightarrow A=\pi {{r}^{2}}…….\left( i \right)$

Therefore, firstly we need to find out the radius, r of the circle. We have been given the radius of the circle in the above question to be equal to $10$ inches.

Therefore, we can write

$\Rightarrow D=10\text{ inches}……..\left( ii \right)$

We know that the radius of a circle is equal to the half of its diameter, that is

$\Rightarrow r=\dfrac{D}{2}$

On substituting the value of the diameter from the equation (ii) in the above equation, we get

$\begin{align}

& \Rightarrow r=\dfrac{10}{2} \\

& \Rightarrow r=5\text{ inches} \\

\end{align}$

Now, we substitute this in the equation (i) to get

\[\begin{align}

& \Rightarrow A=\pi {{\left( 5 \right)}^{2}} \\

& \Rightarrow A=25\pi \\

\end{align}\]

Finally, on substituting $\pi =3.14$ in the above equation we get

\[\begin{align}

& \Rightarrow A=25\times 3.14 \\

& \Rightarrow A=78.5\text{ i}{{\text{n}}^{2}} \\

\end{align}\]

Hence, the area of the given circle is equal to \[78.5\] square inches.

Note: Do not forget to write the unit for the area along with its value. Also, do not make the mistake of substituting the value of the diameter instead of the radius. To avoid this mistake, we can remember the second formula for the area of the circle in terms of its diameter as $A=\dfrac{\pi {{D}^{2}}}{4}$.

Complete step by step answer:

We know that the area of a circle is given by the formula

$\Rightarrow A=\pi {{r}^{2}}…….\left( i \right)$

Therefore, firstly we need to find out the radius, r of the circle. We have been given the radius of the circle in the above question to be equal to $10$ inches.

Therefore, we can write

$\Rightarrow D=10\text{ inches}……..\left( ii \right)$

We know that the radius of a circle is equal to the half of its diameter, that is

$\Rightarrow r=\dfrac{D}{2}$

On substituting the value of the diameter from the equation (ii) in the above equation, we get

$\begin{align}

& \Rightarrow r=\dfrac{10}{2} \\

& \Rightarrow r=5\text{ inches} \\

\end{align}$

Now, we substitute this in the equation (i) to get

\[\begin{align}

& \Rightarrow A=\pi {{\left( 5 \right)}^{2}} \\

& \Rightarrow A=25\pi \\

\end{align}\]

Finally, on substituting $\pi =3.14$ in the above equation we get

\[\begin{align}

& \Rightarrow A=25\times 3.14 \\

& \Rightarrow A=78.5\text{ i}{{\text{n}}^{2}} \\

\end{align}\]

Hence, the area of the given circle is equal to \[78.5\] square inches.

Note: Do not forget to write the unit for the area along with its value. Also, do not make the mistake of substituting the value of the diameter instead of the radius. To avoid this mistake, we can remember the second formula for the area of the circle in terms of its diameter as $A=\dfrac{\pi {{D}^{2}}}{4}$.

Last updated date: 25th Aug 2023

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