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What is the area of the circle with a diameter of 16?
  {\text{A}}{\text{. 8}}\pi \\
  {\text{B}}{\text{. 16}}\pi \\
  {\text{C}}{\text{. 64}}\pi \\
  {\text{D}}{\text{. 128}}\pi \\
  {\text{E}}{\text{. 256}}\pi \\

Last updated date: 20th Jun 2024
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Hint: In order to find the area of a circle, we use the formula for the area of the circle given its measure of the radius. To find the length of radius of the circle we make use of the measure of the diameter of the circle given in the question. Using this data we find the answer.

Complete step-by-step answer:
Given Data,
Diameter of the circle = 16 units

We know the area of a circle is given by the formula,
${\text{A = }}\pi {{\text{r}}^2}$, where r is the radius of the circle.

We know the diameter of a circle is two times the radius of the circle, given by
D = 2r

Given that the diameter of the circle is 16.
Therefore the radius of the circle is given by
$\dfrac{{\text{D}}}{2} = \dfrac{{16}}{2} = 8$
r = 8 units.

Now the area of the circle A is determined as follows:
${\text{A = }}\pi {{\text{r}}^2}$
$ \Rightarrow {\text{A = }}\pi {\left( 8 \right)^2}$
$ \Rightarrow {\text{A = 64}}\pi $
Hence the area of the circle with a diameter of 16 units is 64π square units.
Option C is the correct answer.

Note: In order to solve this type of problems the key is to know the formula of area of a circle and the relation between the diameter and the radius of a circle. The units of measurement of the diameter is not given in the question which is why we just write units next to its measure in numbers, just as a convention. Area of a geometrical figure is always expressed in square units.