Question

The length,breath and thickness of a rectangular sheet metal are 4.234m,1.005m and 2.01cm respectively give the area of the sheet to correct significant figures?

Answer 1

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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. 1) l. 2)b. 3) h

NUMBER. 1)4.234 2)1.005 3)2.01

SIGNIFICANT FIG. 1). 4 2). 4 3). 3

Hence, area and volume both must have 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 × h = 4.234 × 1.005 × 0.0201

= 0.0855 m3

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

I hope, this will help you

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Answer 2

Explanation:

Given:-

Length = 4.234 m

Breadth = 1.005 m

Height (thickness of sheet) = 2.01 cm = 0.0201 m

Solution:-

$Area \: = \: 2(lb \: + \: bh \: + hl) \\ = 2(4.234 \: \times1.005 \: + 1.005 \: \times 0.201 \: + \: 0.201\: \times \: 4.234) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \: 2(4.25517 + 0.0202005 + 0.08551034) \\ = (8.7209478) \\= 8.72 \: {m}^{2}$

Now,

$Volume \: = \: l \: \times \: b \: \times \: h \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4.234 \: \times 1.005 \: \times \: 0.0201 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.0855 \: m ^{3}$

$Hence \: The \: area \: is \: 8.72 \: m ^{2} \: \: and \: \\ Volume \: is \: 0.0855 {m}^{3}$