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To make a sand sculpture Arthur used 2 cm³ of red sand with a density of 4 g/cm³ 7 cm³ of yellow sand with a density of 5 g centimeter and 5 cm³ of brown sand with a density of 6 g cubiccm³ what is the average density of the sculpture in grams per cubic centimeter express your answer as decimal to the nearest 10th.



Answer :

sqdancefan

Answer:

  5.2 g/cm³

Step-by-step explanation:

Given a sculpture consisting of 2 cm³ at 4 g/cm³, 7 cm³ at 5 g/cm³, and 5 cm³ at 6 g/cm³, you want its average density.

Mass

The total mass of the sculpture is the sum of the masses of the components. Each of those is the product of its volume and density.

  red sand: (2 cm³)(4 g/cm³) = 8 g

  yellow sand: (7 cm³)(5 g/cm³) = 35 g

  brown sand: (5 cm³)(6 g/cm³) = 30 g

The total mass of the sculpture is ...

  total mass = 8 g + 35 g + 30 g = 73 g

Volume

The total volume of the sculpture is the sum of the volumes of its parts:

  total volume = 2 cm³ +7 cm³ +5 cm³ = 14 cm³

Average density

The density is the ratio of mass to volume:

  ρ = (total mass)/(total volume) = (73 g)/(14 cm³) = 73/14 g/cm³

  = 5 3/14 g/cm³ ≈ 5.2 g/cm³

The average density of the sculpture is about 5.2 g/cm³.

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