Problem 47 - College Physics

Question

The cover of your physics book measures \(0.274 \mathrm{~m}\) long and \(0.222 \mathrm{~m}\) wide. What is its area in square meters?

Step-by-Step Solution

Answer

The area of the book cover is \(0.060828\, \mathrm{m}^2\).

Step 1: Identify the Measurements

We are given the length and width of the physics book cover. The length is \(0.274\, \mathrm{m}\) and the width is \(0.222\, \mathrm{m}\).

Step 2: Use the Formula for Area

To find the area of a rectangle, we use the formula: \[ \text{Area} = \text{Length} \times \text{Width} \]

Step 3: Plug in the Values

Substitute the given measurements into the area formula: \[ \text{Area} = 0.274\, \mathrm{m} \times 0.222\, \mathrm{m} \]

Step 4: Calculate the Area

Perform the multiplication to calculate the area: \[ \text{Area} = 0.060828\, \mathrm{m}^2 \]

Step 5: State the Final Area

The area of the book cover is \(0.060828\, \mathrm{m}^2\).

Key Concepts

Rectangular Area

When tackling problems involving the area of a rectangle, it's important to understand the basic concept of what the area represents. The area of a rectangular object, like your physics book cover, tells you how much surface space the rectangle has. This is helpful for many practical applications, such as figuring out how much material you would need to wrap or cover an object. The area is determined by the extent of the rectangle's length and width. Therefore:

• The length is one of the longer edges of the rectangle.
• The width is the shorter side of the rectangle.

This area is always expressed in "square" units because it describes a two-dimensional space. Whether you're measuring a book cover, a floor, or a garden plot, when the shape is a rectangle, you'll use the same approach to find the area by considering both its length and width.

Formula for Area

The formula for finding the area of a rectangle is a straightforward one—perfect for quick calculations or solving homework problems.To calculate the area (\(A\)), you'll use the formula:\[A = ext{Length} imes ext{Width}\]Here's what each term in the formula means:

• Length: This represents one of the rectangle's longer sides.
• Width: This stands for the shorter side of the rectangle.

Once you've identified the length and width, simply multiply these two values. This multiplication gives you the total area contained within the rectangle. For example, a physics book with a length of \(0.274 \mathrm{~m}\) and a width of \(0.222 \mathrm{~m}\) would have:\[A = 0.274 \mathrm{~m} \times 0.222 \mathrm{~m} = 0.060828 \mathrm{~m}^2\]It’s a simple and efficient formula, making it easy to handle a variety of rectangular shapes.

Units of Measurement

Units of measurement are crucial when calculating area. Knowing what units are at play helps ensure your answer is meaningful and correct. For area, you'll generally use square units, like square meters ( $m^2$ ), square inches ( $in^2$ ), or square feet ( $ft^2$ ), depending on the size of the object and the context. In the context of your physics book cover:

• Meters: The initial measurements were given in meters, which is a standard unit in the metric system.
• Square Meters: When you calculate the area by multiplying the length and width (in meters), you find the area in square meters ( $m^2$ ).

The square meter denotes a squared area that has one meter on each side. It is a universal unit for area that makes it easy to convey dimensions regardless of the metric system you are using. By using square units, you can easily communicate and compare areas, making them applicable across different regions and projects.