Question

The circumference of a circle is $ 10\pi $ cm, find the radius and the area of the circle. $ \left( {take\,\,\pi = 3.14} \right) $

Answer 1

Hint: In this we first let radius of a circle be ‘r’ then first taking or using formula of circumference of circle equal to given value to find radius of circle and then using this value of radius in formula of area of circle to find value of area of circle and hence required solution of given problem.
Formulas used: Circumference of a circle = $ 2\pi r $ , Area of a circle = $ \pi {r^2} $

Complete step-by-step answer:
Given circumference of a circle is $ 10\pi $ .

Also we know that circumference of a circle is given as = $ 2\pi r $ , where ‘r’ is the radius of the circle.
 $ \Rightarrow C = 2\pi r $
Substituting given value of circumference in above formula we have,
 $
  10\pi = 2\pi r \\
   \Rightarrow r = \dfrac{{10\pi }}{{2\pi }} \\
   \Rightarrow r = 5 \;
  $
Hence, from above we see that the radius of a circle is $ 5\;cm. $
Now, using this area we can find the area of a circle.
We know that area of a circle is given as: $ \pi {r^2} $
 $ A = \pi {r^2} $
Substituting value of ‘r’ calculated above from circumference of circle in above formula of area of circle.
We have
 $ A = \pi {\left( 5 \right)^2} $
Taking value of $ \pi = 3.14 $ , substituting value in above equation. We have,
 $
  A = 3.14 \times 25 \\
  A = 78.5 \;
  $
Therefore, from above we see that area of a circle is $ 78.5\;c{m^2} $
So, the correct answer is “ $ 78.5\;c{m^2} $ ”.

Note: In this type of mensuration problems one must see units of each given terms must be same if not then first make them same and then one should take or choose required formula related to given figure and most important one should do calculation very carefully as any silly mistake may lead to wrong answer.