Calculate the mass of each of the following: a. A sphere of gold with a radius of 10.5 cm. (The volume of a sphere with a radius r is V = (4/3)πr3; the density of gold is 19.3 g/cm^3.)
b. A cube of platinum of edge length 0.021 mm (density = 21.4 g/cm3).
c. 37.3 mL of ethanol (density = 0.798 g/mL).

A.  93,586.6 g

B.  1.982 × 10⁻⁷ g

C.  29.77 g

Explanation:

A.  Find the volume using the given formula.

V = (4/3)πr³

V = (4/3)π(10.5)³

V = (4/3)π(1157.625)

V = 1543.5π

V = 4849.05 cm³

Using the volume and density, solve for mass.

(4849.05 cm³) × (19.3 g/cm³) = 93,586.6 g

B.  Convert mm to cm.

0.021 mm = 0.0021 cm

Use the formula for the volume of a cube.

V = s³

V = (0.0021)³

V = 9.261 × 10⁻⁹ cm³

Using the volume and density, solve for mass.

(9.261 × 10⁻⁹ cm³) × (21.4 g/cm³) = 1.982 × 10⁻⁷ g

C.  You simply use the volume and density to solve for mass.

(37.3 mL) × (0.798 g/mL) = 29.77 g

a) 93598.82 g

b) 1.98 x 10^-7 g

c) 29.76 g

Explanation:

a) radius of gold sphere = 10.5 cm

volume =

V = = 4849.68 cm^3

if the density of gold = 19.3 g/cm^3

mass = density x volume

m = 19.3 x 4849.68 = 93598.82 g = 93.59 kg

b) edge length of platinum cube L= 0.021 mm = 0.0021 cm

Volume = = = 9.26 x 10^9 cm^3

If the density = 21.4 g/cm^3

mass = density x volume

m =  21.4 x 9.26 x 10^-9 = 1.98 x 10^-7 g

c) for a 37.3 mL of ethanol

density = 0.798 g/mL

mass m = 0.798 x 37.3 = 29.76 g

d.) the average kinetic energy of the gas particles is greater in container b because its particles move faster.