# Q 2.11: 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.

Given,

Length, l = 4.234 m ; Breadth, b = 1.005 m; Height, h = 2.01 cm = 0.0201 m

The length has 4 significant figures

The breadth has 4 significant figures

The height has 3 significant figures (Since the number is less than 1, hence zeroes after decimal before the first non-zero integer is insignificant)

We know,

Surface area of a cuboid = 2(l x b + b x h + h x l)

= $2(4.234 \times 1.005 + 1.005 \times 0.0201 + 0.0201 \times 4.234)$

=$2(4.255 + 0.020 + 0.085)$

=  $8.72 \ m^{2}$                (Note: For addition/subtraction, the number of places after the decimal point in the answer is less than or equal to the number of decimal places in every term in the sum; i.e decided by the numbers after the decimal.)

Volume = l x b x h

= $4.234 \times 1.005 \times 0.0201$ = $0.0855 \ m^3$   ($\therefore$ 3 significant digits)

(Note: For Multiplication The LEAST number of significant digits in any number determines the number of significant figures in the answer; i.e decided by the number of significant digits)

The area has three significant values 2, 7 and 8.

The volume has three significant values 5, 5 and 8.

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