Question

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

Answer 1

(a) $1.58\cdot 10^5 g$

The radius of the sphere is:

r = 12.5 cm

So the volume of the sphere of gold is

$V=\frac{4}{3}\pi r^3 = \frac{4}{3}\pi (12.5 cm)^3=8181 cm^3$

The density of gold is

$d=19.3 g/cm^3$

So the mass of the sphere is

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

(b) $2.53\cdot 10^{-6} g$

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

$V=L^3 = (0.0049 cm)^3=1.18\cdot 10^{-7}cm^3$

The density of platinum is

$d=21.4 g/cm^3$

So the mass of the cube is

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

(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

$m=dV=(0.798 g/mL)(67.1 mL)=53.5 g$