Answers to Density Problems

Density = mass
                 volume

1)  What is the volume of a tank that can hold 18 754 Kg of methanol whose density is
      0.788g/cm³?

       v = 2.38 x 10⁷ cm³

2) What is the density of a board whose dimensions are 5.54 cm x 10.6 cm X 199 cm and
     whose mass is 28.6 Kg?

      D = 2.45 g   
                    cm³

3) CaCl₂ is used as a de-icer on roads in the winter. It has a density of 2.50 g/cm³. What is the
     mass of 15.0 L this substance?

     m = 3.75 x 10⁴ g

4) In the Macy's Thanksgiving day parade, 2000, there was a new float, the Cheerios' bee,
    Buzzbee.  The jar of honey it was holding contained  36,763 L of helium.  The honey jar was
    1/10 of the body size.
    What is the volume of the entire float?  If the density of helium is  0.000178 g/cm³, what is the
     mass of the helium for the entire float in Kg?

     v = 367,630 L He

     m = 65.4 Kg

5) My gas tank in my car has a total volume of 68 L.  The manual says the gas gauge light will
    come on when there are only 5 L remaining in the tank and that the car will not be able to
    draw on the last 2 L in the tank.  Practically speaking, what is the functional volume of the gas
    tank?  If I ran out of gas, the car won't go,  and I put in 5 L of gas, what is the total volume of
    gas in my tank?  If 5 L of gas has a mass of  450 Kg, what is the mass of the gas in my tank?
   What is the density of the gas?

     D = m/v

     functional volume of tank is 68L - 2 L = 66 L  gas

     "empty tank" + 5 L = 7 L gas

     m = 630 Kg

     D = 9.0 x 10¹ g  
                           cm³

6) The density of paper is 1.20 g/cm³.  What is the mass of the paper in a notebook that is 76
     mm thick, 215.9 mm wide, and 279.4mm long?  Express your answer in significant
     digits.

     5.5 x 10³ g

7) In pottery class, you throw a pot from a lump of wet clay.  Your pot's mass is 5.5 Kg.  After 
    the pot is fired, it's mass is 4.9 Kg.  The density of wet clay is 1.60 g/cm³ and the density of
    fired clay is 1.36 g/cm³.  What was the volume of your pot before it was fired?  What was
    the volume of the pot after it was fired?  Express your answer in significant digits.

    volume of wet clay is 3.4 x 10³ cm³

    volume of dry clay is 3.6 x 10³ cm³

8) The Italian government is giving Michelangelo's David a bath.  In the newspaper, there was a
     photo of a person working on the statue.  Their hand was half the size of the statue's hand.  
     If the statue is 4.9m³ and the density of marble is 2.76 g/cm³ what is the mass?  Express your
     answer in significant digits.

     mass of marble = 1.4 x 10⁷  g

9) The volume of the aquarium in our classroom is 1890 L.  The density of seawater is 
     1.03g/cm³.  What is the mass of the water in our tank?  Express your answer in significant
     digits.

      mass = 1.95 x 10⁶  g

10) Spanish mahogany is a red, lustrous wood.  It is prized over Honduras mahogany, which
      does have the characteristic red color and similar grain, but is the wood is not as compact
      and has a looser appearance than the Spanish mahogany.  A hope chest made of Honduras
      mahogany has a volume of .648 m³  and a mass of 349 Kg.  An identical hope chest made
      of Spanish mahogany has a mass of 550.8 Kg.  What is the density of Honduras
       mahogany?  What is the density of Spanish mahogany?  Express your answer in significant
      digits.

      density of Honduras mahogany is 0.539 g/cm³

        density of Spanish mahogany is 0.850 g/cm³