Question

What is the approximate area of a circle with a radius of $1.5$?

Answer 1

Hint: Here in this question we want to find the area of a circle and whose radius is equal to $1.5$. To find the area we have a standard formula as $A = \pi {r^2}$. We know the value of $\pi $ and the value of radius is given to us in the question itself. We substitute the known values and determine the area of a circle using the formula.

Complete step by step answer:

To find the area of a circle, we use formula $A = \pi {r^2}$. The radius of the circle is given as $1.5$ units.
By substituting, we get,
$A = \pi {r^2}$
$ \Rightarrow A = \pi {\left( {1.5} \right)^2}$ square units
Now, we know that $1.5 = \dfrac{3}{2}$. So, writing tge expression in this way, we get,
$ \Rightarrow A = \pi {\left( {\dfrac{3}{2}} \right)^2}$ square units
\[ \Rightarrow A = \pi \times \left( {\dfrac{3}{2}} \right) \times \left( {\dfrac{3}{2}} \right)\] square units
\[ \Rightarrow A = \dfrac{9}{4}\pi \] square units
Therefore the area of a circle with a radius $1.5$ units is $\dfrac{{9\pi }}{4}$ square units.
We can substitute the value of $\pi $ to find the area and we can simplify further.
Substituting the value of $\pi $, we have,
\[ \Rightarrow A = \dfrac{9}{4} \times \dfrac{{22}}{7}\] square units
Further simplifying the calculations, we have,
\[ \Rightarrow A = \dfrac{{198}}{{28}}\] square units
Cancelling the common factors in numerator and denominator, we get,
\[ \Rightarrow A = \dfrac{{99}}{{14}}\] square units
Now, we have to express the area of the circle in decimal representation. So, we have,
\[ \Rightarrow A = 7.07\] square units
Hence the area of a circle whose radius is $1.5$ units is $7.07$ square units approximately.

Note:
Students should not get confused between the formula of circumference and area. To avoid confusion we can check the units as circumference has unit as length and area has square of length.