The density of gold is about 20 g/ cm^3 . The density of sand can be estimated at 2.5 g/cm^3. The gold statue can be modeled as a cylinder with height 25 cm and radius 8 cm

In the opening scene of the movie Raiders of the Lost Ark, Indiana Jones replaces a golden statue with a bag of sand. The platform on which the statue is placed is designed to detect the mass of the statue. If the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues.

The density of gold is about 20 g/ cm^3 . The density of sand can be estimated at 2.5 g/cm^3. The gold statue can be modeled as a cylinder with height 25 cm and radius 8 cm.

In terms of pi, what is the mass of sand Indiana Jones needs to avoid triggering the mechanism?

step 1

Find the volume of the gold statue

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

substitute the given values

[tex]V=\pi (8)^{2}(25)[/tex]

[tex]V=600\pi\ cm^3[/tex]

step 2

Find the mass of gold

Remember that the mass is equal to multiply the density by the volume

so

[tex]m=(20)600\pi\\m=12,000\pi\ g[/tex]

step 3

what is the mass of sand Indiana Jones needs to avoid triggering the mechanism?

we know that

The mass of the bah of sand must be equal to the mass of the statue

therefore

The mass of the bag of sand must be equal to

[tex]m=12,000\pi\ g[/tex]