Density Worksheet Answers - Problems 16-20

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16) convert kg to grams: 57.0 kg x (1000 g / 1 kg) = 5.70 x 104 g

determine volume of the copper wire: (5.70 x 104 g) ÷ (8.94 g/cm3) = 6375.8389 cm3

convert mm to cm: 9.50 mm x (1 cm/10 mm) = 0.950 cm

determine length of wire: 6375.8389 cm3 = (3.14159) (0.950 cm)2 h; h = 18077 cm = 1.81 x 104 cm

Note: for the step above, you need to know the formula for the volume of a cylinder.

convert cm to meters: 1.81 x 104 cm x (1 m / 100 cm) = 1.81 x 102 m = 181 m

17) assume the penny occupies 1.00 cm3. This means:

copper occupies 0.06025 cm3 and zinc occupies 0.93975 cm3.

calculate mass of copper: (0.06025 cm3) (8.94 g/cm3) = 0.538635 g
calculate mass of zinc: (0.93975 cm3) (7.14 g/cm3) = 6.709815 g

determine apparent density: 0.538635 g + 6.709815 g = 7.24845 g
since this mass is in 1.00 cm3, the answer is 7.25 g/cm3

18) calculate volume of ice: (1.42 x 1018 cm2) (1.61 x 105 cm) = 2.2862 x 1023 cm3

calculate mass of ice: (2.2862 x 1023 cm3) (0.92 g/cm3) = 2.1 x 1023 g

19) Object A has a larger volume than Object B.

20) The solution to this problem involves the concept of buoyancy.

determine the mass of the cube: (45.0 mL) (0.900 g/cm3) = 40.5 g

The cube will float when 40.5 g of liquid is displaced. We need to know what volume of the liquid weighs 40.5 g.

volume of liquid: (40.5 g) ÷ (1.36 g/mL) = 29.8 mL

This means that 29.8 mL of the cube is submerged (this is the answer to the question), displacing 40.5 g of the liquid. The rest of the cube (45.0 - 29.8) is above the surface of the liquid.

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