Analyzing the Setup
We are given the dimensions of a strip: length L=10.5 cm, breadth b=0.05 mm, and thickness t=6.0μm.
Notice how the units are all over the place! Before we can even think about calculating the volume, we need to bring everything to a common ground. Since our options are in cubic centimeters (cm3), it makes perfect sense to convert all measurements to centimeters.
Unit Conversion and Precision
Let's convert the breadth and thickness:
b=0.05 mm=0.05×10−1 cm=0.005 cm
t=6.0μm=6.0×10−4 cm=0.0006 cm
Now, here is the catch. This isn't just a math problem; it's a physics problem about precision. We must count the significant figures for each measurement.
For length L=10.5, we have 3 significant figures.
For breadth b=0.05, leading zeros do not count, so we have exactly 1 significant figure.
For thickness t=6.0, the trailing zero after the decimal is significant, giving us 2 significant figures.
The Master Equation
The rule for multiplication is strict: your final answer can only be as precise as your least precise measurement.
Since our breadth has only 1 significant figure, our final volume must also be rounded to exactly 1 significant figure. Let's calculate the raw volume first:
V=L×b×t
V=10.5×0.005×0.0006
V=0.0000315 cm3=3.15×10−5 cm3
Final Calculation
We have our raw volume, but we must enforce our precision constraint. We need to round 3.15×10−5 to 1 significant figure.
Looking at the first digit, 3, the next digit is 1. Since 1 is less than 5, we simply drop the rest, leaving us with:
V=3×10−5 cm3
This perfectly matches option (D). Always remember, a chain is only as strong as its weakest link, and a calculation is only as precise as its least precise measurement!
