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

`Length = 25cm`

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 = (Mass)/(Volume)`

Make Volume the subject of formula

`Volume = (Mass)/(Density)`

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

`Volume = (1,05\ kg)/(4.2\ g/cm^3)`

Convert 1.05 kg to grams

`Volume = (1.05 * 1000\ kg)/(4.2\ g/cm^3)`

`Volume = (1050 \ kg)/(4.2\ g/cm^3)`

`Volume = (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

`(250cm^3)/(0.4cm) = (0.4cm * Area)/(0.4cm)`

`(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

`√(625cm^2) = Length`

`25cm = Length`

`Length = 25cm`

Hence, the length of the square brass is 25cm