A) An iron wire (density = 7.87 g/cm 3 ) has a diameter of 0.20 mm. If a sample

Question

A) An iron wire (density = 7.87 g/cm3) has a diameter of 0.20 mm. If a sample of this iron wire has a mass of 28 g, how long is this wire?

l= _____ ft ?

B) The density of osmium is reported by one source to be 22610 kg/m3 . What is this density in g/cm3?

C) What is the mass of a block of osmium measuring 10.0 cm × 7.2 cm × 9.4 cm?

D)Diamonds are measured in carats, and 1 carat = 0.200 g. The density of diamond is 3.51 g/cm3.

- What is the volume of a 6.0-carat diamond?   

Volmue = ______ cm3 ?

-What is the mass in carats of a diamond measuring 2.4 mL?   

mass = _______ carrots ?

Explanation / Answer

A)first we find the volume of Iron:
28 grams Fe @ 1cm3 / 7.87 grams = 3.5578 cm3 of Iron

this wire with a diameter of 0.2 mm, has a radius of 0.1 mm,...
this radius of 0.1 mm => => 0.01 cm

the formula for the volume of the wire is the same as the formula of any cylinder:
volume = (area of a crossection) (height or length)
volume = (pi r2) h

3.5578 cm3 = [(3.14)(0.01 cm)^2] (length)

3.5578 cm3 = (3.14)(0.0001 cm2) (length)

length = 3.5578 cm3 / (3.14)(0.0001 cm2)

length = 11330.57 cm

B)Given Density of Osmium = 22610 kg/m3

                                             = 22610 *10 3 / 106 g/cm3

                                            = 22.610 g/cm3

C) First Volume of Osmium block = length *height * breath

                                                    = 10.0 cm × 7.2 cm × 9.4 cm

                                                      = 676.8 cm3

mass = Deansity * volume = 22.610 g/cm3 x 676.8 cm3 = 15302.448 grams

D)Six carat daimond weight = 6*0.2g =1.2gram

So volume = mass/density = 1.2/3.51 0.34188cm3

Mass of 2.4ml daimond = 3.51*2.4 = 8.424 grams (since 2.4ml = 2.4cm3

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