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------------------------------------------------ The circumference of the hub cap of a tire is 79.63 centimeters. Find the area of this hub cap using [tex]3.14[/tex] for [tex]\pi[/tex].

1. Calculate the radius of the hub cap using the formula for circumference:
[tex]C = 2\pi r[/tex]

2. Use the radius to find the area of the hub cap with the formula:
[tex]A = \pi r^2[/tex]

Explain how the area of the hub cap would change if the circumference were smaller.

Round the final answer to the nearest whole number. Round all intermediate values to the nearest thousandth as needed.

The area of this hub cap is about _____ square centimeters.

Answer :

Recall that the circumference of a circle is given by the following formula:

[tex]C=2\pi r,[/tex]

where r is the radius of the circle.

We are given that:

[tex]79.63cm=2\pi r,[/tex]

therefore:

[tex]r=\frac{79.63}{2*\pi}cm.[/tex]

Now, the area of a circle is given by the following formula:

[tex]A=\pi r^2,[/tex]

Therefore, the area of the hub cap is:

[tex]A=\pi *(\frac{79.63cm}{2})^2*\frac{1}{\pi^2}\approx505cm^2.[/tex]

Answer:

[tex]\begin{equation*} 505cm^2. \end{equation*}[/tex]

Given that the radius of the circle and the circumference are proportionally related, if the circumference is smaller then the radius is smaller. The area is proportionally related to the radius squared, therefore, a smaller circumference implies a smaller radius which implies a smaller area.

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