Use the formulas for the area and the circumference of a...

Use the formulas for the area and the circumference of a circle in Table 2.4 on page 170 to solve. Unless otherwise indicated, round all circumference and area calculations to the nearest whole number. Hardwood flooring costs $\$ 10.00$ per square foot. How much will it cost (to the nearest dollar) to cover the dance floor shown in the figure with hardwood flooring? (image cannot copy)

Use the formulas for the area and the circumference of a circle in Table 2.4 on page 170 to solve. Unless otherwise indicated, round all circumference and area calculations to the nearest whole number.
Hardwood flooring costs $\$ 10.00$ per square foot. How much will it cost (to the nearest dollar) to cover the dance floor shown in the figure with hardwood flooring?
(image cannot copy)

Key Concepts

Rounding Principles

Rounding is the process of adjusting numbers to a desired degree of precision, such as to the nearest whole number. It is often used in real-world applications to simplify calculations, ensure clarity in reporting, or match practical constraints like pricing or measurement limitations.

Cost Calculation Based on Area

In many practical applications, the total cost is determined by multiplying a unit cost (such as cost per square foot) by the total area that needs to be covered. This method allows one to translate area measurements into financial figures, providing a direct way to estimate expenses for materials or services.

Area of a Circle

This concept involves calculating the area of a circle using the formula A = ?r², where r is the radius of the circle. It is a fundamental geometry formula used to determine how much two-dimensional space a circle occupies, and it is essential when dealing with problems that require covering or filling circular regions.

Transcript

00:01 This question deals with finding the area of an irregular shape, the surface area of an irregular shape, and then doing a calculation to calculate the cost of applying a hardwood floor to it.

00:15 So this shape, although not drawn out very well, it contains two shapes that we know how to calculate the area of, shape one being a rectangle, and then shape two being a circle.

00:28 And in this case, they're two half circles, which we can imagine sandwiching them together to create one full circle.

00:37 So let's start with shape one.

00:39 Shape one is a rectangle.

00:40 The area of a rectangle is equal to the length times the width.

00:44 So in this case, we know the length is 60, and we got to figure out this distance that will highlight in yellow from here to here.

00:55 Well, it's just, it's kind of tough to see in this diagram here, but from here to here, from there to down here, that would be 20 feet because it's a radius.

01:07 That means this is 20 feet, so the entire thing then would be 40 feet.

01:12 So i can take the 60, multiply it by 40, and that's going to give me the area of shape 1, the rectangle.

01:19 So that's 2 ,400 square feet or feet squared.

01:24 So there's shape 1.

01:25 Now shape 2 is a circle.

01:27 The formula for the area of a circle is pi r squared.

01:30 And now i'm going to imagine i'm actually, this is part of shape 2...

Please give Ace some feedback