Question

1. in the lab you are given a rectangular metal object that has a mass of 7.86 x 10^(-3) kg and its dimensions are 4.928 x 10^5 mm by 2.423 x 10^(-5) km by 5.0 cm.

a. sketch what the object looks like with its dimensions.

b. calculate the volume of the object in cm^3.

c. determine the density of the object in units of g/cm^3.

Explanation:

Step1: Convert dimensions to cm

First, convert all dimensions to cm.
$1\ mm = 0.1\ cm$, so $4.928\times 10^{5}\ mm=4.928\times 10^{5}\times0.1\ cm = 4.928\times 10^{4}\ cm$.
$1\ km = 10^{5}\ cm$, so $2.423\times 10^{- 5}\ km=2.423\times 10^{-5}\times10^{5}\ cm = 2.423\ cm$. The third - dimension is already $5.0\ cm$.

Step2: Calculate the volume

The volume $V$ of a rectangular object is $V = l\times w\times h$.
$V=(4.928\times 10^{4}\ cm)\times(2.423\ cm)\times(5.0\ cm)$
$V = 4.928\times2.423\times5.0\times10^{4}\ cm^{3}$
$V=59.47792\times 10^{4}\ cm^{3}\approx5.95\times 10^{5}\ cm^{3}$

Step3: Convert mass to g

The mass $m = 7.86\times 10^{-3}\ kg$. Since $1\ kg = 1000\ g$, then $m=7.86\times 10^{-3}\times1000\ g = 7.86\ g$.

Step4: Calculate the density

The density $
ho=\frac{m}{V}$.
$
ho=\frac{7.86\ g}{5.95\times 10^{5}\ cm^{3}}\approx1.32\times 10^{-5}\ g/cm^{3}$

Answer:

a. A rectangular - shaped object with one side approximately $4.928\times 10^{4}\ cm$ (a very long side), another side $2.423\ cm$, and the third side $5.0\ cm$. You can draw a rectangle - like box with these relative side - lengths labeled.
b. $5.95\times 10^{5}\ cm^{3}$
c. $1.32\times 10^{-5}\ g/cm^{3}$