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

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​

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  1. [tex]Length = 25cm[/tex]

    Step-by-step explanation:

    Given

    Brass Shape: Square

    [tex]Density = 4.2g/cm^3[/tex]

    [tex]Mass = 1.05kg[/tex]

    [tex]Height = 4mm[/tex]

    Required

    Determine the length of the plate

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

    [tex]Density = \frac{Mass}{Volume}[/tex]

    Make Volume the subject of formula

    [tex]Volume = \frac{Mass}{Density}[/tex]

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

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

    Convert 1.05 kg to grams

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

    [tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]

    [tex]Volume = \frac{1050 \ kg}{4.2\ g/cm^3}[/tex]

    [tex]Volume = 250cm^3[/tex]

    Next is to determine the Area of the brass;

    [tex]Volume = Height * Area[/tex]

    Substitute 250cm³ for Volume and 4mm for Height

    [tex]250cm^3 = 4mm * Area[/tex]

    Convert mm to cm

    [tex]250cm^3 = 4 * 0.1cm * Area[/tex]

    [tex]250cm^3 = 0.4cm * Area[/tex]

    Divide both sides by 0.4cm

    [tex]\frac{250cm^3}{0.4cm} = \frac{0.4cm * Area}{0.4cm}[/tex]

    [tex]\frac{250cm^3}{0.4cm} =Area[/tex]

    [tex]625cm^2 = Area[/tex]

    [tex]Area = 625cm^2[/tex]

    Lastly, we'll calculate the length of the brass

    Since the brass is square based;

    [tex]Area = Length^2[/tex]

    Substitute 625cm² for Area

    [tex]625cm^2 = Length^2[/tex]

    Take square root of both sides

    [tex]\sqrt{625cm^2} = Length[/tex]

    [tex]25cm = Length[/tex]

    [tex]Length = 25cm[/tex]

    Hence, the length of the square brass is 25cm

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