How would I solve these physical science questions

Question

The questions are:

 

What volume of iron has the same mass as 100 cm3 of lead? [lead= 11.4 g/cm3, iron= 7.87 g/cm3]

 

You buy 6 million dollars' worth of gold at $40 per gram.

a. What is the mass of the gold? Is it light enough for you to carry?

b. The density of the gold is 19.3 g/cm3. What is the volume of the gold? Will it fit into a briefcase that is 40 cm x 25 cm x 10cm?

 

 

I am really stuck, if you could help me on how to solve I would appreciate.

Answer 1

For the first question, you have to use dimensional analysis to cancel out units to arrive at the correct unit, which in this case is the mass of iron.

100 cm³(11.4 g/1 cm³) = 1140 g lead This cancels out the unit cm³ of lead.

1140 g lead = 1140 g iron It says in the problem iron has the same mass as lead

1140 g iron (1 cm³/7.87 g) = 145 g iron This will cancel out the unit g to give us the volume.

For the second question, you will again use dimensional analysis:

a. $6,000,000 (1 gram/ $40) = 150,000 grams = 150 kg Cancel out the dollar units.

This equates to roughly 330 pounds( 1 kg = 2.2 pounds). This is too heavy to carry.

b. 150,000 grams (1 cm³/19.3 g) = 7,772 cm^3.

The dimensions of the briefcase are 10,000 cm^3. Therefore, the volume of gold will fit inside the briefcase.