A typical dollar bill is 15.50 cm by 6.50 cm.
Calculate the surface area in square meters, square centimeters and square nanometers
The Correct answer and Explanation is:
To find the surface area of a typical dollar bill, we can use the formula for the area of a rectangle, which is:
[
\text{Area} = \text{length} \times \text{width}
]
Given Measurements
- Length = 15.50 cm
- Width = 6.50 cm
Step 1: Calculate the Surface Area in Square Centimeters
Using the formula, we substitute the values:
[
\text{Area} = 15.50 \, \text{cm} \times 6.50 \, \text{cm}
]
[
\text{Area} = 100.75 \, \text{cm}^2
]
Thus, the surface area of the dollar bill is 100.75 cm².
Step 2: Convert to Square Meters
To convert square centimeters to square meters, we use the conversion factor that (1 \, \text{m}^2 = 10,000 \, \text{cm}^2):
[
\text{Area in m}^2 = \frac{100.75 \, \text{cm}^2}{10,000}
]
[
\text{Area in m}^2 = 0.010075 \, \text{m}^2
]
Therefore, the surface area in square meters is 0.010075 m².
Step 3: Convert to Square Nanometers
To convert square centimeters to square nanometers, we note that (1 \, \text{cm}^2 = 10^{16} \, \text{nm}^2):
[
\text{Area in nm}^2 = 100.75 \, \text{cm}^2 \times 10^{16}
]
[
\text{Area in nm}^2 = 1.0075 \times 10^{18} \, \text{nm}^2
]
Thus, the surface area in square nanometers is 1.0075 × 10¹⁸ nm².
Summary of Results
- Surface area in square centimeters: 100.75 cm²
- Surface area in square meters: 0.010075 m²
- Surface area in square nanometers: 1.0075 × 10¹⁸ nm²
Explanation
In this calculation, we first established the dimensions of a dollar bill and applied the area formula for rectangles. After calculating the area in square centimeters, we converted this measurement into square meters and square nanometers by using appropriate conversion factors. These conversions are essential for expressing measurements in various scientific contexts, as different applications may require data in specific units. For example, while square meters are often used in construction and real estate, square nanometers are more common in nanotechnology and materials science, highlighting the bill’s dimensions across vastly different scales. Understanding how to convert between these units is crucial for accuracy in both practical and theoretical applications.