A square brass plate of side x cm is 1 mm thick and weighs 4725 g. If one cc of brass weights 8.4 g, find the value of x.

Given,

Side of square brass plate = $x$ cm

Here, l = $x$ cm and b = $x$ cm

Thickness of plate = 1 mm = $\dfrac{1}{10}$ = 0.1 cm

We know that,

Volume of the plate = l × b × h

Substituting the values

= $x$ × $x$ × 0.1

= $0.1x^2$ cm³

Given,

Weight of 1 cm³ of brass = 8.4 g

∴ Weight of $0.1x^2$ cm³ of brass = 8.4 x $0.1x^2$ g

But weight of square brass plate is given as 4725 g

$\therefore 8.4 \times 0.1x^2 = 4725 \\[1em] \Rightarrow x^2 = \dfrac{4725}{8.4 \times 0.1} \\[1em] \Rightarrow x^2 = \dfrac{472500}{84 \times 1} \\[1em] \Rightarrow x^2 = 5625 \\[1em] \Rightarrow x = \sqrt{5625} = 75.$

Hence, x = 75.