Final answer:
The question is about Mathematics, focusing on surface area and significant figures at the High School level. Answers need to be rounded to the correct place value, with attention to dimensional consistency in formulas and correct expression of scientific notation
Step-by-step explanation:
The subject of the question is Mathematics, specifically focused on surface area and significant figures which are typically topics at the High School level. For part (b) of a multi-part question, a student would need a calculator to find the exact surface area, which yields an initial answer of 201.867. However, the final answer must be rounded to the hundredths place due to the specifics of the problem's requirements. Since the digit in the thousandths place is a 7 (which is more than 5), it would round up, giving a final answer of 201.87. When it comes to significant figures, the rules differ slightly based on the context of the figures given. To demonstrate proper rounding with significant figures, the answer from an example calculation, 921.996, must be rounded to the hundredths place, becoming 922.00 because of the significant figures rule.
Students also need to be aware of how to express answers with the correct number of significant figures, as seen in the calculation and conversion examples provided. For instance, when multiplying two numbers, the final answer should have the same number of significant figures as the number with the least amount of significant figures in the problem.
Fundamental geometric formulas such as those for the area of a triangle, which is (1/2) × base × height, must be used with attention to dimensional consistency, as shown in the dimensional analysis problems. The same goes for proper expression of numbers in scientific notation, which is also essential in reporting measurements to an appropriate degree of precision.