QuestionFind the density of glass with $2.5 \frac{\mathrm{g}}{\mathrm{cm}^{3}}$ in $\frac{\mathrm{kg}}{\mathrm{m}^{3}}$ .

Studdy Solution

STEP 1

Assumptions1. The density of the glass is $.5 \frac{\mathrm{g}}{\mathrm{cm}^{3}}$ . We want to convert this density to $\frac{\mathrm{kg}}{\mathrm{m}^{3}}$
3. We know that $1 \mathrm{g} =0.001 \mathrm{kg}$ and $1 \mathrm{m} =100 \mathrm{cm}$

STEP 2

First, we need to convert the mass from grams to kilograms. We can do this by multiplying the density by the conversion factor from grams to kilograms.
$Density_{kg/m^{}} = Density_{g/cm^{}} \\times Conversion\, factor_{g\, to\, kg}$

STEP 3

Now, plug in the given values for the density and the conversion factor to calculate the new density.
$Density_{kg/m^{3}} =2.5 \frac{\mathrm{g}}{\mathrm{cm}^{3}} \\times0.001 \frac{\mathrm{kg}}{\mathrm{g}}$

STEP 4

Calculate the new density.
$Density_{kg/m^{3}} =2. \times0.001 \frac{\mathrm{kg}}{\mathrm{cm}^{3}} =0.002 \frac{\mathrm{kg}}{\mathrm{cm}^{3}}$

STEP 5

Next, we need to convert the volume from cubic centimeters to cubic meters. We can do this by multiplying the density by the conversion factor from cubic centimeters to cubic meters. Since we are dealing with cubic measurements, we need to cube the conversion factor.
$Density_{kg/m^{3}} = Density_{kg/cm^{3}} \\times (Conversion\, factor_{cm\, to\, m})^{3}$

STEP 6

Now, plug in the given values for the density and the conversion factor to calculate the new density.
$Density_{kg/m^{3}} =0.0025 \frac{\mathrm{kg}}{\mathrm{cm}^{3}} \\times (100 \frac{\mathrm{cm}}{\mathrm{m}})^{3}$

STEP 7

Calculate the new density.
$Density_{kg/m^{3}} =0.0025 \frac{\mathrm{kg}}{\mathrm{cm}^{3}} \\times1000000 \frac{\mathrm{cm}^{3}}{\mathrm{m}^{3}} =2500 \frac{\mathrm{kg}}{\mathrm{m}^{3}}$ The density of the glass in $\frac{\mathrm{kg}}{\mathrm{m}^{3}}$ is $2500 \frac{\mathrm{kg}}{\mathrm{m}^{3}}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms