Question

If the density of silver is 10.5 g/mL, what is the mass of 1.00 cubic ft?

Answer 1

The mass of the silver is 297 kg.

Explanation:

Let's take this step-by-step.

Step 1. Convert 1 ft to centimetres

`1 color(red)(cancel(color(black)("ft"))) × (12 color(red)(cancel(color(black)("in"))))/(1 color(red)(cancel(color(black)("ft")))) × "2.54 cm"/(1 color(red)(cancel(color(black)("in")))) = "30.5 cm"`

Step 2. Convert `"1 ft"^3` to cubic centimetres

`1 color(red)(cancel(color(black)("ft"^3))) × (("30.5 cm")/(1 color(red)(cancel(color(black)("ft")))))^3 = "28 300 cm"^3`

Step 3. Calculate the mass of the silver

`"Mass of Ag" = "28 300" color(red)(cancel(color(black)("cm"^3color(white)(l) "Ag"))) × "10.5 g Ag"/(1 color(red)(cancel(color(black)("cm"^3color(white)(l)"Ag")))) = "297 000 g Ag"`

Step 4. Convert the mass of silver to kilograms

`"Mass of Ag" = "297 000" color(red)(cancel(color(black)("g Ag"))) × "1 kg Ag"/(1000 color(red)(cancel(color(black)("g Ag")))) = "297 kg Ag"`