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How do you find the area of a circle in terms of pi if the diameter is \[2.1{\text{ }}m\]?

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Last updated date: 04th Mar 2024
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IVSAT 2024
Answer
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Hint: First we will mention the formula for evaluating the area of circle $ A = \pi {r^2} $ . Then we will evaluate all the required terms from the given question. Then we will apply the formula and evaluate the area of the circle in terms of pi.

Complete step by step solution:
We will mention the formula for the area of the circle.
 $ A = \pi {r^2} $ .
Here, the value of $ \pi $ is a number that approximately equals $ 3.14\, $ and $ r $ is the radius of the sphere.
Remember that to use the formula, we need the value of the radius. Since the radius is half of the diameter, we can find the value of the radius by dividing $ 2.1 $ with $ 2 $ .
Hence, the radius will be,
 $
  r = \dfrac{d}{2} \\
  r = \dfrac{{2.1}}{2} \\
  r = 1.05 \;
  $
With the radius, $ r = 1.05 $ inches, we can calculate the area of the circle.
 $
  A = \pi {r^2} \\
  A = \pi {(1.05)^2} \\
  A = \pi (1.1025) \\
  A = 1.1025\pi \,{m^2} \;
  $
Now, it is important to include the unit. Since, the radius is in metres. The volume will be in square metres. Therefore, the area of the circle is $ 1.1025\pi \,{m^2} $ .
So, the correct answer is “ $ 1.1025\pi \,{m^2} $ ”.

Note: A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
Always be sure that all of the measurements are in the same unit before computing the area. Also remember that every line that passes through the circle forms the line of reflection symmetry. The circle formula in the plane is given by $ {(x - h)^2} + {(y - k)^2} = {r^2} $
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