Question

A square based brass plate in 4mm high and has a mass of 1.05kg. The density of the brass is 4.2g/cm3, calculate the length of the plate in centimeters​

Answer 1

Answer:

$Length = 25cm$

Step-by-step explanation:

Given

Brass Shape: Square

$Density = 4.2g/cm^3$

$Mass = 1.05kg$

$Height = 4mm$

Required

Determine the length of the plate

First, we need to calculate the Volume of the Brass using

$Density = \frac{Mass}{Volume}$

Make Volume the subject of formula

$Volume = \frac{Mass}{Density}$

Substitute 1.05kg for Mass and 4.2g/cm³ for Density

$Volume = \frac{1,05\ kg}{4.2\ g/cm^3}$

Convert 1.05 kg to grams

$Volume = \frac{1.05 * 1000\ kg}{4.2\ g/cm^3}$

$Volume = \frac{1050 \ kg}{4.2\ g/cm^3}$

$Volume = \frac{1050 \ kg}{4.2\ g/cm^3}$

$Volume = 250cm^3$

Next is to determine the Area of the brass;

$Volume = Height * Area$

Substitute 250cm³ for Volume and 4mm for Height

$250cm^3 = 4mm * Area$

Convert mm to cm

$250cm^3 = 4 * 0.1cm * Area$

$250cm^3 = 0.4cm * Area$

Divide both sides by 0.4cm

$\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}$

$\frac{250cm^3}{0.4cm} =Area$

$625cm^2 = Area$

$Area = 625cm^2$

Lastly, we'll calculate the length of the brass

Since the brass is square based;

$Area = Length^2$

Substitute 625cm² for Area

$625cm^2 = Length^2$

Take square root of both sides

$\sqrt{625cm^2} = Length$

$25cm = Length$

$Length = 25cm$

Hence, the length of the square brass is 25cm