Question

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

Answer 1

Thickness of brass plate = 1 mm or 0.1 cm
As the plate is in square shape, so the length and breath are same.
Length = x cm, breadth = x cm. and thickness = 0.1 cm
Volume = x² × 0.1 cm³
Given that 1 cu cm of brass has weight = 8.4 g
So, total weight = 8.4 × x² × 0.1
= 0.84x² gram
The weight of the plate = 4725 grams (Given)
⇒ 0.84x² = 4725
x² = 4725/0.84
x² = 5625
x = √5625
x = 75 cm
So the value of x is 75 cm

Answer 2

A squared brass plate will have four equal sides (since, it is squared shape)

So, its area = x² cm².

Since the height (thickness) of the brass plate is 1 mm or 1/10 cm, we can say that the volume of the actual plate = (x² × 1/10) cm³ = x²/10 cm³.

Given that, the weight of 1 cm³ of brass is 8.4 g.

Volume of the actual plate = (4725/8.4) cm³ = 562.5 cm³

BY CONDITION,

x²/10 = 562.5

Or, x² = 5625

Or, x = √5625

Or, x = 75 cm

Hence, the value of x is 75 cm.