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Question -

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



Answer -

Length of sheet,┬аl┬а= 4.234 m

Breadth of sheet,┬аb┬а= 1.005 m

Thickness of sheet,┬аh┬а= 2.01 cm = 0.0201 m

The given table lists the respective significant figures:

Quantity

Number

Significant Figure

l

4.234

4

b

1.005

4

h

0.0201

3

Hence, area and volume both must have least significant figuresi.e., 3.

Surface area of the sheet = 2 (l┬а├Ч┬аb┬а+┬аb┬а├Ч┬аh┬а+┬аh┬а├Ч┬аl)

= 2(4.234 ├Ч 1.005 + 1.005 ├Ч 0.0201 + 0.0201 ├Ч 4.234)
= 2(4.25517 + 0.0202005 + 0.0851034)
= 2 ├Ч 4.36
= 8.72 m2

Volume of the sheet =┬аl┬а├Ч┬аb┬а├Ч┬аh

= 4.234 ├Ч 1.005 ├Ч 0.0201

= 0.0855 m3

This number has only 3 significant figures i.e., 8, 5, and 5.

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