Question

copy (1) circles, proportional relationship, scale drawing
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a circle has a diameter that measures 8\frac{1}{4} inches (in.) in length. what is the area of the circle? use the π button on your calculator and round your answer to the nearest hundredth.

Explanation:

Step1: Find the radius

The radius $r$ of a circle is half of the diameter $d$. Given $d = 8\frac{1}{4}=\frac{33}{4}$ inches, so $r=\frac{d}{2}=\frac{33}{8}$ inches.

Step2: Use the area formula

The area formula of a circle is $A = \pi r^{2}$. Substitute $r=\frac{33}{8}$ into the formula: $A=\pi\times(\frac{33}{8})^{2}=\pi\times\frac{1089}{64}$.

Step3: Calculate the value

Using the $\pi$ - button on the calculator, $A=\frac{1089\pi}{64}\approx\frac{1089\times 3.14159}{64}\approx\frac{3411.19151}{64}\approx53.30$.

Answer:

$53.30$