Question

What is the area of a circle with a radius of 10 cm?

Answer 1

Hint: Assume the radius of the circle as r. Now, use the formula for the area of a circle given as $A=\pi {{r}^{2}}$ where A is the area of the circle. Substitute the value of $\pi $ equal to 3.14 for the ease of calculation. Write the unit of area as centimeter square to get the complete answer.

Complete step by step solution:
Here we have been provided with the radius of a circle equal to 10 cm and we are asked to find its area. We can draw a rough diagram of a circle with radius 10 cm as shown below.

Now, let us assume the radius of the circle as r. We know that the area of a circle is given by the formula $A=\pi {{r}^{2}}$ where A is the area of the circle. So, substituting the value of radius (r = 10 cm), given in the question, in the formula for the area we get,
$\begin{align}
  & \Rightarrow A=\pi {{\left( 10 \right)}^{2}} \\
 & \Rightarrow A=100\pi \\
\end{align}$
Substituting the value of $\pi $ equal to 3.14 we get,
$\begin{align}
  & \Rightarrow A=100\times 3.14 \\
 & \Rightarrow A=314 \\
\end{align}$
Now, we can see that the unit of radius is centimeter so the unit of area will be centimeter square. So we get,
$\therefore A=314c{{m}^{2}}$
Hence, the area of the given circle is $314c{{m}^{2}}$.

Note: Note that we have taken the value of $\pi $ equal to 3.14. We did this so that we can calculate the area easily as the radius is a multiple of 10 and not 7. If it were multiple of 7 then we would have used the value $\pi =\dfrac{22}{7}$. Remember that you must include the unit of area in the end because a physical quantity is of no meaning without its unit.