Indiana Jones is in a temple searching for artifacts. He finds a gold sphere with a radius of 2 cm sitting on a pressure sensitive plate. To avoid triggering the pressure plate, he must replace the gold with something of equal mass. The density of gold is 19.3.103 kg/m3, and the volume of a sphere is V = 4/3 Ar3. Indy has a bag of sand with a density of 1,602 kg/m3.

(A) What volume of sand must he replace the gold sphere with? If the sand was a sphere, what radius would it have?

### Leave a Comment

You must be logged in to post a comment.

Answer:Volume of Sand = 0.4 m³

Radius of Sand Sphere = 0.46 m

Explanation:First we need to find the volume of gold sphere:

Vg = (4/3)πr³where,

Vg = Volume of gold sphere = ?

r = radius of gold sphere = 2 cm = 0.02 m

Therefore,

Vg = (4/3)π(0.2 m)³Vg = 0.0335 m³Now, we find mass of the gold:

ρg = mg/Vgwhere,

ρg = density of gold = 19300 kg/m³

mg = mass of gold = ?

Vg = Volume of gold sphere = 0.0335 m³

Therefore,

mg = (19300 kg/m³)(0.0335 m³)mg = 646.75 kgNow, the volume of sand required for equivalent mass of gold, will be given by:

ρs = mg/Vswhere,

ρs = density of sand = 1602 kg/m³

mg = mass of gold = 646.75 kg

Vs = Volume of sand = ?

Therefore,

1602 kg/m³ = 646.75 kg/VsVs = (646.75 kg)/(1602 kg/m³)Vs = 0.4 m³Now, for the radius of sand sphere to give a volume of 0.4 m³, can be determined from the formula:

Vs = (4/3)πr³0.4 m³ = (4/3)πr³r³ = 3(0.4 m³)/4πr³ = 0.095 m³r = ∛(0.095 m³)r = 0.46 m