Question

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

Answer 1

Length of sheet, l = 4.234 m
Breadth of sheet, b = 1.005 m
Thickness of sheet, h = 2.01 cm = 0.0201 m
The given table lists the respective significant figures:
Quantity: l , Number: 4.234, Significant Figure: 4
Quantity: b , Number: 1.005, Significant Figure: 4
Quantity: h , Number: 2.01, Significant Figure : 3
Hence, area and volume both must have the least significant figures i.e., 3.
Surface area of the sheet = 2 (l × b + b × h + h × l) = 2(4.234 × 1.005 + 1.005 × 0.0201 + 0.0201 × 4.234) = 2 (4.25517 + 0.02620 + 0.08510) = 2 × 4.360 = 8.72 m2
Volume of the sheet = l × b × = 4.234 × 1.005 × 0.0201 = 0.0855 m3
This number has only 3 significant figures i.e., 8, 5, and 5.