My question has to do with science and a little bit of math as well. The question is "What is the mass of an object that has a density of 7.45 g/mL & a volume of 36.45 mL? " Can you explain how...

My question has to do with science and a little bit of math as well. The question is "What is the mass of an object that has a density of 7.45 g/mL & a volume of 36.45 mL? " Can you explain how I am supposed to solve this? Thank you. 

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

We assume that the object has the same density throughout, e.g. it is of uniform density.

The density is represented by `rho` , the Greek letter rho. (Though it can also be represented by the Latin `D` .) Using `m` for the mass and `V` for the unit volume, the formula for the density is `rho=m/V` .

Here the volume is measured in mL and the density in g/mL, so the mass will be measured in grams.

Solving the formula for the mass, `m` , we get `m=rho V` .

`m=7.45 "g"/"mL"*36.45"mL"=271.5525g`

Note that the volume units divide out leaving the units for mass.

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The mass of the object is 271.55 grams

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The mass of the object will be typically measured with a scale while the volume can be measured either by direct measurement (e.g. the volume of basic solids) or by fluid displacement. Density can be measured by hydrostatic weighing.

This is the technique reportedly used by Archimedes to solve a problem: a king had commissioned a crown to be made of gold, but he suspected (correctly) that the smith had replaced some of the gold with an equal weight of another metal. The weight of the crown was correct but the problem was to find the density. Archimedes realized that you could find the volume of water displaced by the correct amount of gold and this would be the same for any configuration (shape) of the solid.

Sources:
tduellman's profile pic

tduellman | (Level 1) Adjunct Educator

Posted on

Density (p) = mass (m) / volume (v)

You are given two of the variables (d) and (v) and you need to solve for the third, (m).

To do this re-arrange the equation to solve for (m).

mass (m) = density (p) * volume (v)

(m) = 7.45 g/mL * 36.45 mL 

(m) = 271.5525 g

chemrock's profile pic

chemrock | College Teacher | eNotes Newbie

Posted on

My question has to do with science and a little bit of math as well. The question is "What is the mass of an object that has a density of 7.45 g/mL & a volume of 36.45 mL? " Can you explain how I am supposed to solve this? Thank you. 

Mass of object=m=?

Density=d=7.45g/mL

Volume=v=36.45mL

Density(d)=mass(m)/Volume(v)

mass(m)=Density(d)*Volume(v)=7.45g/mL*36.45mL=271.55g

so mass of the object is 271.55g

jmyates's profile pic

Jessica | Middle School Teacher | eNotes Newbie

Posted on

Density (D) equals the mass (M) of an object divided by the volume (V) of the object: D = M/V

To solve for mass, you would rearrange the equation by multiplying both sides by volume. V x D = (M/V) x V. The volume on the right side of the equation cancel each other out, leaving V x D = M.

M = V x D

M = 36.45 mL x 7.45 g/mL = 272 g (three significant figures)

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