Question

How do you find the area of a circle whose diameter is $6$ feet?

Answer 1

As we know that to find the area of a circle, the formula $A = \pi {r^2}$is used and since here, we are given the diameter of the circle, we need to figure out the relation between the diameter and the radius so that we can calculate the radius from the given diameter to put it into the formula of area.

Complete step by step solution:
(i)
We are given the diameter of a circle
$d = 6$ft.
As we know that diameter is twice the radius i.e.,
$d = 2r$
Putting $d = 6$ft. in the equation, we will get,
$6 = 2r$
For finding the value of $r$, the equation will be:
$\dfrac{6}{2} = r$
Therefore,
$r = 3$ft.
(ii)
Now, as we have to calculate the area of the circle, we will use the formula
$A = \pi {r^2}$
where, $\pi$ is a constant whose value is $3.141$
$r$ is the radius of the circle
And, $A$ is the area of the circle
So, putting the value of radius in the formula we get,
$A = 3.141 \times {3^2} \\\ A = 3.141 \times 9 \\\ A = 28.269 \\\$
Hence, area of the circle with diameter $6$ft. is $A = 28.269$sq. ft.

Note: Always remember to write the units with the answer as it is very important. Like here, the unit for radius and diameter is feet while the unit for the area of the circle is square feet (sq. ft. written in short).
This question could also be directly solved without calculating the radius with the formula $A = \dfrac{{\pi {d^2}}}{4}$ where $A$ is the area and $d$ is the diameter of the circle. This formula is derived from the original formula itself by substituting $r$ as $\dfrac{d}{2}$.