Question : A plate on the square base made of brass is of length $x$ cm and width 1 mm. The plate weighs 4725 g. If 1 cm3 of brass weighs 8.4 g, then the value of $x$ is:
Option 1: 75 cm
Option 2: 76 cm
Option 3: 72 cm
Option 4: 74 cm
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Correct Answer: 75 cm
Solution :
We know that,
Volume = $\frac{\text{Weight} }{\text{Density}}$
Substituting the given values,
$\therefore$ Volume = $\frac{4725\;\mathrm{g}}{8.4\;\mathrm{g/cm^3}}$ = 562.5 cm
3
____(i)
Volume = l × w × h, where l is the length, w is the width, and h is the height.
(1 mm = 0.1 cm)
Volume = $x$ × $x$ × 0.1 = $x ^2$ × 0.1 ____(ii)
Equating equation (i) and (ii), we get,
$x ^2$ × 0.1 = 562.5
$\therefore x = \sqrt{5625}$ = 75
Hence, the correct answer is 75 cm.
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