Question

The radius of a circle is stated as $$2.12cm$$. Its area should be written as
a). $$14c{m}^2$$
b). $$14.1c{m}^2$$
c). $$14.11c{m}^2$$
d). $$14.1124c{m}^2$$

Answer 1

Hint: To solve this question first we assume the area of the circle as a variable. to find the area of the circle we use the formula of the area of the circle. Then we put the value of the radius in the formula and put the value of the constant term that is $$\pi$$ and on further calculation, we get the value of the area of the circle.

Complete step-by-step solution:
Given,

Radius of the circle $$r=2.12cm$$
To find,
Area of the circle with the given radius.
Let the area of the circle is $$A$$
So using the formula of area of circle
$$A=\pi r^2$$
On putting the value of radius of the circle.
$$A=\pi {\left(2.12cm\right)}^2$$
On further calculation.
$$A=\pi \times 4.4944c{m}^2$$
On putting the value of the constant term that is $$\pi$$
The value of $$\pi =3.14$$
On putting this value
$$A=3.14\times 4.4944c{m}^2$$
On further calculating
$$A=14.1124c{m}^2$$
Final answer:
The area of the circle have radius $$r=2.12cm$$ is
$$\Rightarrow A=14.1124c{m}^2$$ which is option (D)

Note: This question is asking us to find the value of the area of the circle. It may be possible that the area of the circle is given and we are asking for the radius of the circle. On finding we got two values of the radius they are positive signs and negative signs. We choose the positive sign because the distance is never negative. It may be possible that they are asking for the mate required to cover the whole circle then also we have to find the area and say that is the area of the mate.