Question

Find the area of a circle with diameter \[6\] unit.

Answer 1

Hint: The diameter of the circle is given, from there we can find the radius as the diameter is twice the radius and hence with the radius the area can be found.

Complete step by step solution:

Let the area of the circle be represented by \[A\].
Let the diameter of the circle be represented by \[D\].
Let the radius of the circle be represented by \[R\].
First, find out the radius of the circle:
Given diameter \[ = \] \[6\] unit.
Diameter of a circle is twice its radius,
\[\therefore \] radius \[\left( R \right)\] \[ = \] \[\dfrac{D}{2}\] (where \[D\] ids the diameter of the circle.)
\[ \Rightarrow \] \[R\] \[ = \] \[\dfrac{6}{2}\] unit
\[ \Rightarrow \] \[R\] \[ = \] \[3\] unit
The area of a circle is given by the formula:
\[A = \pi {R^2}\] ; \[\left[ {\pi = \dfrac{{22}}{7}} \right]\]
Substitute the value of \[R\] in the formula for the area:
\[A = \pi {R^2}\]
\[ \Rightarrow \] \[A = \pi {\left( 6 \right)^2}\] square unit.
\[ \Rightarrow \] \[A = \pi \left( {6 \times 6} \right)\] square unit.
\[ \Rightarrow \] \[A = 36\pi \] square unit.
Substitute value of \[\pi \]:
\[ \Rightarrow \] \[A = 36 \times \left( {\dfrac{{22}}{7}} \right)\] square unit.
\[ \Rightarrow \] \[A = \dfrac{{792}}{7}\] square unit.

Hence, the area of the circle is \[\dfrac{{792}}{7}\] square unit.

Note: Observe the question carefully whether the radius or the diameter is given. The formula stated is applicable for the radius only, so if the diameter is given then convert it to the radius and don’t substitute directly in the formula.
\[\pi \] is a constant defined as the ratio of the circumference of a circle to the diameter of the circle. Its value is equal to \[\dfrac{{22}}{7}\] or \[3.14\](approximately).