Question

Saira is using the formula for the area of a circle to determine the value of LaTeX: \piπ. She is using the expression LaTeX: Ar^{-2}\:A r − 2where LaTeX: A\:=\:50.265\:A = 50.265and LaTeX: r\:=\:4\:r = 4. Use a calculator to evaluate Saira's expression to find her approximation for the value of LaTeX: \pi\:πto the nearest thousandth.

Answer 1

Given:

Area of a circle, A=50.265 sq. units.

Radius of circle, r = 4 units.

To find:

The value of π to the nearest thousandth.

Solution:

Formula for area of a circle is

$A=\pi r^2$

$\dfrac{A}{r^2}=\pi$

$Ar^{-2}=\pi$

Now, using $Ar^{-2}$ expression, we can find the value of π.

$\pi=50.265904(4)^{-2}$

$\pi=\dfrac{50.265904}{4^2}$

$\pi=\dfrac{50.265904}{16}$

$\pi=3.141619$

Approximate the value to the nearest thousandth (three digits after decimal).

$\pi\approx 3.142$

Therefore, the approximated value of π is 3.142.