Question

Find the area of a circle with a circumference of 88 cm.

Answer 1

Hint: The circumference of a circle of radius r is given by,\[ = 2\pi r\]. We try to find r from the given equation. Then using that r we will get the area of the circle.

Complete step by step answer:

Given a circle of circumference 88 cm
We know Circumference of a circle \[ = 2\pi r\]
Where r is the radius of the circle
Circumference \[ = 2\pi r\] (the value of \[\pi \] is\[\dfrac{{22}}{7}\])
On substituting the values, we get,
\[88{\text{ }} = {\text{ }}2{\text{ }} \times \dfrac{{22}}{7} \times {\text{ }}r\]
On simplifying we get,
\[\begin{array}{*{20}{l}}
  { \Rightarrow r{\text{ }} = {\text{ }}\dfrac{{88 \times 7}}{{22 \times 2}}} \\
  { \Rightarrow r{\text{ }} = {\text{ }}14{\text{ }}cm}
\end{array}\]
The radius of the circle is 14 cm.
We know Area of the circle \[ = \pi {r^2}\]
Area \[ = \pi {r^2}\]
Area of circle \[ = \dfrac{{22}}{7} \times 14 \times 14\]
On simplifying we get,
 \[ = {\text{ }}22{\text{ }} \times {\text{ }}2{\text{ }} \times {\text{ }}14\]
 \[ = {\text{ }}44{\text{ }} \times {\text{ }}14\]
Area of circle \[ = 616c{m^2}\]
Therefore, the area of the circle is \[ = 616c{m^2}\]

Note: The area of the circle is given as \[\pi {r^2}\]. We use the value of \[\pi \] as\[\dfrac{{22}}{7}\]for simpler results and easier calculations but the point value i.e. \[3.14\] can also be used for calculations, and also, on the other hand, the radius needs to be in the proper unit to get the answer correctly. As we are using cm in this problem, we are going to use cm in the whole solution.