Question

A circular garden has an area of 100$\pi $ feet squared. What is the circumference of the garden in feet?

Answer 1

Hint:Here the area of the circle is given and we have to find the circumference of the circle so we will first find the radius of the circle then find circumference.

Formula used:Area of circle = $\pi r^2$ and Circumference of circle =$2\pi r$.

Complete step-by-step answer:

Here area of a circle = 100 $\pi $
And we know that the area of a circle is given by $\pi {r^2}$ where r is the radius of the circle.
Thus, $\pi {r^2}= 100 \pi $
$r^2=100$
$r=+10 \, \text{or} -10$
We should consider +10 as radius should always be positive.
Therefore, r = 10 feet.
Now we know that circumference of the circle is given by $2\pi r$ where r is the radius of the circle.
$\therefore 2\pi r = 2 \times 3.14 \times 10 = 62.8$ feet.
This is the required circumference of the circle in feet.

Note:The locus of the point such that its distance from the fix point is constant, called the locus of the circle. The fixed point is called the centre of the circle and it is denoted by ‘O’ and the constant distance is called radius of the circle and it is denoted by ‘r’. Thus the circle is denoted by C (O, r).The boundary of a circle is called circumference of the circle. Circumference of the circle = $\pi d = \pi .2r = 2\pi r$. Students should remember all the properties and formulas of circles for solving these types of questions.