Question

What would the area of a circle be if the circumference is $20 \pi$?

Answer 1

Hint: In this type of question we have to use the concept of area and circumference of a circle. We know that if the circumference of the circle is given then by using the formula of circumference of a circle that is \[\text{Circumference = }2\pi r\] we can find out the value of \[r\]. Then by using this \[r\]and the formula of area of a circle that is \[\text{Area = }\pi {{r}^{2}}\] we can obtain the area of the given circle.

Complete step by step solution:
Now here we have to find the area of a circle if its circumference is 20pi that is \[20\pi \].
As we know that, circumference of a circle is given by \[2\pi r\]
\[\Rightarrow \text{Circumference = }2\pi r\]
Now substituting the given value of the circumference we get,
\[\Rightarrow \text{20}\pi \text{ = }2\pi r\]
\[\Rightarrow \dfrac{20\pi }{2\pi }=r\]
\[\Rightarrow 10=r\]
Hence, the radius of the given circle is 10.
Now, to find the area of the given circle we use the formula of area of a circle
\[\Rightarrow \text{Area = }\pi {{r}^{2}}\]
We know that \[\pi \] has a constant value \[\dfrac{22}{7}\]
\[\Rightarrow \text{Area = }\dfrac{22}{7}\times {{\left( 10 \right)}^{2}}\]
\[\Rightarrow \text{Area = }\dfrac{22\times 100}{7}\]
\[\Rightarrow \text{Area }\approx \text{ }314\]
Hence the area of a circle be \[314uni{{t}^{2}}\] if the circumference is \[20\pi \].

Note: In this type of question we have to note that a unit is not given hence we have to write the area of the circle as \[314uni{{t}^{2}}\]. Also students have to take care that as we have to find the area of a circle which depends on the value of \[r\] so we have to select a formula for circumference in terms of radius that is in terms of \[r\].