Practice: A copper wire (density = 8.96 g/cm^{3}) has a diameter of 0.32 mm. If a sample of this copper wire has a mass of 21.7 g, how long is the wire?

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Classification of Matter | 18 mins | 0 completed | Learn Summary |

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Intensive vs. Extensive Properties | 14 mins | 0 completed | Learn |

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The **density of geometric objects** generally includes spheres, cubes and cylinders.

Concept #1: When given the mass of a geometric object you can relate it to its volume and density.

Example #1: The density of silver is 10.5 g/cm^{3}. What is the mass (in kilograms) of a cube of silver that measures 0.56 m on each side?

Practice: A copper wire (density = 8.96 g/cm^{3}) has a diameter of 0.32 mm. If a sample of this copper wire has a mass of 21.7 g, how long is the wire?

Practice: If the density of a certain spherical atomic nucleus is 1.0 x 1014 g/cm^{3} and its mass is 3.5 x 10^{-23} g, what is the radius in angstroms? (Å= 10^{−10} m)

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An aluminum sphere contains 8.66 x 1022 aluminum atoms. What is the sphere’s radius in centimeters? The density of aluminum is 2.70 g/cm3 . Recall that the volume of a sphere is given by the formula: 4/3 π r31.418 cm30.699 cm0.339 cm0.822 cm7.8586 x 10-1 cm

The density of gold is 19.31 g/cm 3. A rectangular bar of gold has a mass of 66.75 g and measures 3.04 cm width and 25.5 cm in height. What is the length of the gold bar?a) 0.0446 cm b) 0.0550 cm c) 0.0189 cm d) 0.0592 cm

The proton has a radius of 1.0 x 10 -13 cm and a mass of 1.7 x 10 -24 g. Determine the density of a proton for a sphere. Volume is equal to (4/3) π r 3.A. 3.4 x 10 21 g/cm 3B. 1.7 x 10 39 g/cm 3C. 5.9 x 10 12 g/cm 3D. 4.1 x 10 14 g/cm 3

A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm3?

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately 1.0 X 10-13 cm. The hydrogen atom itself has a radius of approximately 52.9 pm. What fraction of the space within the atom is occupied by the nucleus?

Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass. If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 5.00 cm radius?

Neutron stars are composed of solid nuclear matter, primarily neutrons. Assume the radius of a neutron is approximately 1.0 x 10–13 cm, and calculate the density of a neutron. [ Hint: For a sphere V = (4/3)πr 3.] Assuming that a neutron star has the same density as a neutron, calculate the mass (in kg) of a small piece of a neutron star the size of a spherical pebble with a radius of 0.10 mm.

A cylindrical tube has a length that is 15.2 cm and is filled with bromine liquid. If the mass of the bromine is 112.3 g and has a density of 25.3 g/mL, then what is the inner diameter of the glass tube? ( V = π • r2 • h )

(a) Three spheres of equal size are composed of aluminum (density = 2.70 g/cm 3), silver (density = 10.49 g/cm3), and nickel (density = 8.90 g/cm3). List the spheres from lightest to heaviest.

A cube of osmium metal 1.500 cm on a side has a mass of 76.31 g at 25 °C. What is its density in g/cm3 at this temperature?

A cylindrical rod formed from silicon is 16.8 cm long and has a mass of 2.17 kg. The density of silicon is 2.33 g/cm3. What is the diameter of the cylinder? (The volume of a eylinder is given by πr2h, where r is the radius, and h is its length.)

Silicon for computer chips is grown in large cylinders called “boules” that are 300 mm in diameter and 2 m in length, as shown. The density of silicon is 2.33 g/cm3. Silicon wafers for making integrated circuits are sliced from a 2.0 m boule and are typically 0.75 mm thick and 300 mm in diameter. (a) How many wafers can be cut from a single boule? (b) What is the mass of a silicon wafer? (The volume of a cylinder is given by πr2h, where r is the radius and h is its height.)

A copper refinery produces a copper ingot weighing 150 lb. If the copper is drawn into wire whose diameter is 8.25 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3 (Assume that the wire is a cylinder whose volume is V = πr2h, where r is its radius and h is its height or length.)

A copper refinery produces a copper ingot weighing 150 lb. If the copper is drawn into wire whose diameter is 7.50 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3. (Assume that the wire is a cylinder whose volume V = πr 2h , where r is its radius and h is its height or length.)

A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately 1.0 g/mL, will a block of material having a volume of 1.2 x 104 in3 and weighing 350 lb float or sink when placed in a reservoir of water?

For a material to float on the surface of water, the material must have a density less than that of water (1.0 g/mL) and must not react with the water or dissolve in it. A spherical ball has a radius of 0.50 cm and weighs 2.0 g. Will this ball float or sink when placed in water? (Note: Volume of a sphere = 4/3πr3.)

A star is estimated to have a mass of 2 x 1036 kg. Assuming it to be a sphere of average radius 7.0 x 105 km, calculate the average density of the star in units of grams per cubic centimeter.

A rectangular block has dimensions 2.9 cm x 3.5 cm x 10.0 cm. The mass of the block is 615.0 g. What are the volume and density of the block?

The density of osmium (the densest metal) is 22.57 g/cm3. If a 1.00-kg rectangular block of osmium has two dimensions of 4.00 cm x 4.00 cm, calculate the third dimension of the block.

A copper wire (density = 8.96 g/cm3) has a diameter of 0.25 mm. If a sample of this copper wire has a mass of 22 g, how long is the wire?

The density of osmium is reported by one source to be 22610 kg/m3. What is this density in g/cm3? What is the mass of a block of osmium measuring 10.0 cm x 8.0 cm x 9.0 cm?

A sheet of copper is 18.0 in x 7.00 in and a mass of 0.0318 g. Given that the density of copper is 8.96 g/cm3. What is the thickness of the copper sheet?a. 282 nmb. 4.4 x 10-6 nmc. 0.044 nmd. 43.7 nme. 3.51 x 103 nm

A gold ingot weighs 5.50 lbs. If the density of gold is 19.31 g/cm 3, and the length and width of the ingot are 12.0 cm and 3.00 cm respectively, what is the height of the ingot?A) 10.2 cm B) 1.34 × 103 cm C) 3.59 cm D) 6.50 × 10-3 cm

A cube of aluminum metal contains 3.35 x 1023 atoms. The density of aluminum is 2.70 g/cm3. What is the length of the edge of the cube? Recall, volume = length 3 (for a cube).A) 1.77 cmB) 5.56 cmC) 2.70 cmD) 15.0 cm

An aluminum sphere contains 8.55 x 10 22 aluminum atoms. What is the sphere's radius in centimeters? The density of aluminum is 2.70 g/ cm3. Recall that the volume of a sphere is given by the formula: 4/3 π r3 A. 1.4187 cm 3B. 0.697 cmC. 0.339 cmD. 0.822 cmE. 7.8583 x10-1 cm

A rectangular wooden block, 22 cm x 13.2 cm x 4.4 cm, has a mass of 1562.0 g. The density of the wood in kg/m3 is:A) 1.2 x 10-1 kg/m3B) 1.2 x 102 kg/m3C) 1.2 x 103 kg/m3D) 1.2 x 109 kg/m3E) 8.2 x 10-4 kg/m3

A certain cylinder has a diameter of 5.0 in and a height of 5 in. Calculate the volume (in cubic centimeters) of the cylinder. (Vcylinder = π r 2h)If the density of the cylinder is 25 g/mL, what is its mass (in kg)?

If a box measuring 16.80 cm x 14.12 cm x 29.44 cm has a mass of 871 g at a given temperature, what is the density?A. 0.0105 g/cm3B. 0.125 g/cm3C. 5.15 g/cm3D. 8.02 g/cm3E. Not enough information is given.

Titanium metal, density of 4.54 g/cm3, is used to make golf clubs. A rectangular bar of titanium which weighs 45.7 g measures 1.84 cm in length and 2.24 cm in width. What is the height of the bar?A) 50.3 cmB) 2.44 cmC) 252 cmD) 12.3 cmE) 4.09 cm

The density of iron is 7.87g/ml . What is the mass of a 5.00 cm * 4.00cm * 1.00cm block of iron?

An osmium sphere contains 1.289 x 10 23 osmium atoms and has a radius 0.755 cm. The molar mass of osmium is 190.23 g•mol-1. What is the density of osmium? Recall that the volume of a sphere is given by the formula: 4/3 π r 3a. 22.6 g/cm 3 b. 6.24 g/cm 3c. 1.80 g/cm 3d. 0.822 g/cm 3

The estimated mass of the planet Jupiter is 1.90 × 10 27 kg and the density is believed to be 1.34 g/cm3. If Jupiter were a perfect sphere, what would be its diameter?A) 6.96 × 107 m B) 1.39 × 107 m C) 1.39 × 108 m D) 6.96 × 106 m

A spherical ball of lead has a diameter of 5.0 cm. What is the mass of the sphere if lead has a density of 11.34 g/cm3? (The volume of a sphere is (4/3)πr3, where r is the radius.)

A metallurgist wants to gold-plate a surface with the following dimensions: 2.5 in x 6.5 in. The gold plating must be 0.0010 in thick. How many grams of gold (d = 19.3 g/cm3) are required?

A 1.00-μm thick layer of gold is plated on a medallion that is 4.00 cm in diameter and 2.00 mm thick. What is the volume (cm3) of gold plated? If the density of gold is 19.3 g/cm3, what is the mass (grams) of the gold plated on the medallion?

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