A block of lead, with dimensions 2.0 dm x 8.0 cm x 35 mm, has a mass of 6.356 kg. How do you calculate the density of lead in #g/(cm^3)#?

2 Answers
May 13, 2018

Answer:

#"11.35 g/cm"^3#

Explanation:

  • Length #"= 2.0 dm = 20 cm"#
  • Breadth #"= 8.0 cm"#
  • Height #"= 35 mm = 3.5 cm"#

Volume of block

#"V = ℓ · b · h = 20 cm × 8.0 cm × 3.5 cm = 560 cm"^3#

Density of lead is

#"Density" = "Mass"/"Volume" = "6356 g"/("560 cm"^3) = "11.35 g/cm"^3#

May 13, 2018

Answer:

#11.35g/(cm^3)#

Explanation:

So first, #density = (mass)/(volume#

Starting with the volume portion, we need to have all of our units in #cm# since that's what the question asks for

#1 dm = 10 cm#

#2.0cancel(dm)# x #(10cm)/(1cancel(dm)# = #20cm#

The #8.0# is already in #cm# so we don't need to do anything, however, we need to convert the #35mm#

#1mm# = #0.1cm#
#35cancel(mm# x #(0.1cm)/(1cancel(mm)# = #3.5cm#

Now we can calculate the volume using #cm# and multiply all of our dimensions

#Volume# = #L# x #W# x #H#

#V# = #20cm# x #8.0cm# x #3.5cm#
#V# = #560cm^3#

Now the mass portion, we need our units in grams (#g#)

Convert #kg# to #g#

#1kg# = #1000g#

#6.356cancel(kg)# x #(1000g)/(1cancel(kg)# = #6356g#

So now we divide #6356g# by #560cm^3# to get our answer

#(6356g)/(560cm^3)# = #11.35g/(cm^3)#