A brass plate has a square base with length \(x\)cm and thickness 1 mm. The weight of the plate is 4725 grams. If the weight of 1 cubic cm of brass is 8.4 grams, what is the value of \(x\)?

Given:
Base is square of side $x$ cm
Thickness = 1 mm = $0.1$ cm
Weight = 4725 g
Density = 8.4 g/cm³

Step 1: Use formula

Weight = Volume × Density

So,
Volume = $\frac{4725}{8.4}$

Step 2: Calculate volume

$\frac{4725}{8.4} = 562.5 \text{ cm}^3$

Step 3: Volume of plate

Volume = base area × thickness
$= x^2 \times 0.1$

So,
$x^2 \times 0.1 = 562.5$

Step 4: Solve

$x^2 = 5625$

$x = \sqrt{5625} = 75$

 Final Answer: 75