Question

lesson 8 practice problems
1 the picture shows a circle divided into 12 equal wedges, which are rearranged.
the radius of the circle is r, and its circumference is 2πr. how does the picture help
to explain why the area of the circle is πr²?
2 a paper plate has a radius of 4.5 inches. what is the area of the plate?
3 jada paints a circular table that has a diameter of 37 inches. what is the area of the table?

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Find the radius of the paper - plate

Given that the radius of the paper - plate \(r = 4.5\) inches.

Step3: Calculate the area of the paper - plate

Substitute \(r = 4.5\) into the formula \(A=\pi r^{2}\).
\(A=\pi\times(4.5)^{2}=\pi\times20.25\approx 3.14\times20.25 = 63.585\) square inches.

Step4: Find the radius of the circular table

Given that the diameter of the circular table \(d = 37\) inches. Since \(r=\frac{d}{2}\), then \(r=\frac{37}{2}=18.5\) inches.

Step5: Calculate the area of the circular table

Substitute \(r = 18.5\) into the formula \(A = \pi r^{2}\).
\(A=\pi\times(18.5)^{2}=\pi\times342.25\approx3.14\times342.25 = 1074.665\) square inches.

Answer:

The area of the paper - plate is approximately \(63.585\) square inches. The area of the circular table is approximately \(1074.665\) square inches.