Chapter 1 Problem, Problem # 1.1 (Find the area of rectangular plate having length 21.3 ± 0.2 cm and with 9.80 ± 0.10 cm.)

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Class XI / HSC-Ι丨Chapter # 1丨Problems

Problem # 1.1

Find the area of rectangular plate having length 21.3 ± 0.2 cm and with 9.80  ± 0.10 cm.

Data:

Length =  L = 21.3 ± 0.2 cm

With = W =  9.80  ± 0.10 cm

Formula

A = L × W

Find Maximum Probable Area

Length =  L = 21.3 + 0.2 = 21.5 cm

With = W =  9.80 + 0.10 = 9.9 cm

A_max = L × W

A_max = 21.5 × 9.9

A_max = 212.83 cm²

After reducing to 2 Significant figures

A_max = 213 cm²

Find Minimum  Probable Area

Length =  L = 21.3 - 0.2 = 21.1 cm

With = W =  9.80 + 0.10 = 9.7 cm

A_min = L × W

Amin = 21.1 × 9.7

Amin = 204.67 cm²

After reducing to 2 Significant figures

A_max = 205 cm²

Find average of two values.

A_av = (213 + 205 ) / 2

A_av = 209 cm²

Difference b/w average value with maximum and minimum value:         

213-209 = + 4

205-209 = - 4

Hence the area will be:

A = 209 ± 4 cm²