Be sure to answer all parts. Calculate the mass of each of the following: (a) a sphere of gold with a radius of 12.5 cm. (The volume of a sphere with a radius r is V = (4/3)πr3; the density of gold is 19.3 g/cm3.) × 10 gEnter your answer in scientific notation. (b) a cube of platinum of edge length 0.049 mm (density = 21.4 g/cm3). × 10 gEnter your answer in scientific notation. (c) 67.1 mL of ethanol (density = 0.798 g/mL). g

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skyluke89 skyluke89 · Answer 1 · 2019-07-18T09:35:27+02:00

(a) [tex]1.58\cdot 10^5 g[/tex]

The radius of the sphere is:

r = 12.5 cm

So the volume of the sphere of gold is

[tex]V=\frac{4}{3}\pi r^3 = \frac{4}{3}\pi (12.5 cm)^3=8181 cm^3[/tex]

The density of gold is

[tex]d=19.3 g/cm^3[/tex]

So the mass of the sphere is

[tex]m=dV=(19.3 g/cm^3)(8181 cm^3)=1.58\cdot 10^5 g[/tex]

(b) [tex]2.53\cdot 10^{-6} g[/tex]

The length of one side of the cube is

L = 0.049 mm = 0.0049 cm

So the volume of the cube of platinum is

[tex]V=L^3 = (0.0049 cm)^3=1.18\cdot 10^{-7}cm^3[/tex]

The density of platinum is

[tex]d=21.4 g/cm^3[/tex]

So the mass of the cube is

[tex]m=dV=(21.4 g/cm^3)(1.18\cdot 10^{-7} cm^3 )=2.53\cdot 10^{-6} g[/tex]

(c) 53.5 g

The volume of the ethanol is

V = 67.1 mL

While its density is

d = 0.798 g/mL

So the mass of the ethanol is

[tex]m=dV=(0.798 g/mL)(67.1 mL)=53.5 g[/tex]