An area is measured to be 800 cm? What is this in square inches? (HINT: lin = 2.54cm) (Spts)
The correct answer and explanation is:
To convert 800 square centimeters (cm²) into square inches (in²), use the conversion factor between centimeters and inches. Since 1 inch = 2.54 centimeters, we must square this to convert area: 1 in2=(2.54)2 cm2=6.4516 cm21\ \text{in}^2 = (2.54)^2\ \text{cm}^2 = 6.4516\ \text{cm}^2
Now divide the given area in square centimeters by this conversion factor: 800 cm2÷6.4516=124.02 in2800\ \text{cm}^2 ÷ 6.4516 = 124.02\ \text{in}^2
Correct answer: 124.02 square inches
To understand the conversion from square centimeters to square inches, it’s important to recognize how units behave during area conversions. Length conversions use a linear factor (such as 2.54 cm per inch), but area conversions require squaring that factor, since area is a two-dimensional measurement.
In this case, since the original area is in cm² and we are converting to in², the relationship between the two units comes from squaring the linear conversion between inches and centimeters. This gives the area conversion factor as 1 in² = 6.4516 cm².
By dividing 800 cm² by 6.4516, we determine how many square inches fit into that space. This results in 124.02 in². The process is precise and important in fields such as engineering, construction, and science where different measurement systems are often used.
To avoid errors, always ensure the correct conversion factor is squared when dealing with area and cubed when dealing with volume. Keeping track of units and applying the correct dimensional change helps maintain accuracy and consistency in all calculations involving conversions.