A plate on square base made of brass is of length $x$ c and width 1 mm. The plate weights 4725gm. If 1 cubic cm of brass weights 8.4 gram. then the value of $x$ is [SSC—CHSL (10+2) Exam, 2015]

### Concept & Density and Volume The volume of a 3D object can be found by dividing its total mass by its density. For a rectangular prism or square-based plate, the volume is also the product of its length, breadth, and height/thickness. $$Volume = \frac{Total\ Weight}{Density} = Length \times Breadth \times Height$$ ### Step-by-Step Solution * Given: Total weight = 4725 gm, Density = 8.4 gm/cm$^3$. * First, find the total volume of the brass plate: Volume = $\frac{4725}{8.4} = 562.5$ cm$^3$. * The plate has a square base of length $x$ cm. (Note: "c" in the question implies cm based on standard units). Since the base is square, both length and breadth are $x$ cm. * The thickness (width) is given as 1 mm. We must convert this to cm to match the other units: 1 mm = 0.1 cm. * Set up the volume equation: Volume = Base Area $\times$ Thickness = $x \times x \times 0.1$. * Equate the two volume expressions: $0.1x^2 = 562.5$. * Solve for $x^2$: $x^2 = \frac{562.5}{0.1} = 5625$. * Taking the square root gives $x = 75$. ### Exam Strategy & Shortcut Instead of long division for $\frac{4725}{8.4}$, recognize that you will eventually divide by 0.1 (the thickness). You can compute $\frac{4725}{0.84} = 5625$ directly. Knowing your square roots speeds this up: $75^2 = 5625$. ### Common Pitfall Forgetting to convert the thickness from millimeters to centimeters before multiplying. Using 1 instead of 0.1 will result in $x^2 = 562.5$, which does not yield a clean integer root. ### Final Answer Therefore, the correct answer is **75**.