Question

Convert 13 in.2 to cm²
a) 33.02 cm²
b) 84.5 cm²
c) 2 cm²
d) 0.5 cm²

Answer 1

To convert 13 in.² to cm², one must square the conversion factor of 2.54 cm/in. Multiplying 13 in.² by 6.4516 cm²/in² results in approximately 84.5 cm². Therefore, the correct option is (b) 84.5 cm².

Step-by-step explanation:

To convert 13 in.² to cm², we need to use the conversion factor for areas between inches and centimeters. Remember, 1 inch is equivalent to 2.54 centimeters. Thus, when converting from square inches to square centimeters, we must square the linear conversion factor (2.54 cm/in) to account for the area conversion.

Here is the step-by-step calculation:

1. Multiply the area value in square inches by the conversion factor, squared: 13 in.² x (2.54 cm/in)².
2. Perform the squaring of the conversion factor: (2.54 cm)² = 6.4516 cm²/in².
3. Now, multiply 13 in.² by 6.4516 cm²/in²: 13 in.² x 6.4516 cm²/in² = 83.8708 cm².

The closest answer to our result, rounded to one decimal place (as none of the options exactly match), is 84.5 cm², which is an option (b).