Question

If the area of a circle is 78.5 $c{m^2}$, Find its circumference. (Take $\pi = $3.14).

Answer 1

Hint: In this question, the area of a circle is given. From this we will easily find the radius of the circle, by assuming its radius as r units and equating area with the given value of area. Then finally we will put the value of radius in the formula of circumference of a circle.

Complete step-by-step answer:
Let r be the radius of the circle.
Given, area of a circle = 78.5 $c{m^2}$
Area of circle = $\pi {r^2}$
$ \Rightarrow \pi {r^2} = 78.5c{m^2}$
$ \Rightarrow {r^2} = \dfrac{{78.5}}{{3.14}}$ (Putting the value of $\pi $ = 3.14)
$ \Rightarrow {r^2} = 25$
$\therefore r = 5$
Circumference of a circle = $2\pi r$
$ = 2 \times 3.14 \times 5 = 31.4$ cm.
Thus, the circumference of a circle is 31.4 cm.

Note: Any geometrical shape has its own area. A circle closed plane geometric shape in a two – dimensional plane. The radius of the circle is the line which joins the center of the circle to the outer boundary. It is represented by ‘r’ and ‘R’. The diameter of the circle is the line which divided the circle into two equal halves. It is double the radius of a circle and it is represented by ‘d’ and ‘D’; d = 2r. The area is the region occupied in the shape in a two – dimensional plane. Area of a circle is $\pi {r^2}$ where $\pi $ = $\dfrac{{22}}{7}$ or 3.14 and r is the radius. The circumference of a circle is the length of the boundary of the circle. The length of rope which wraps around the boundary of a circle then it is equal to its circumference. Circumference of a circle $ = 2\pi r$, where r is the radius of a circle.