Question

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\text{ g/cm}^320 g/cm
3
20, start text, space, g, slash, c, m, end text, cubed. The density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm
3
2, point, 5, start text, space, g, slash, c, m, end text, cubed. The solid-gold statue can be modeled as a cylinder with height 15\text{ cm}15 cm15, start text, space, c, m, end text and radius 4\text{ cm}4 cm4, start text, space, c, m, end text.
In terms of \piπpi, what is the volume of sand Indiana Jones needs to avoid triggering the mechanism?

Answer 1

1920π

Explanation:

First, you need to find the volume of the statue in terms of pi.

Volume of cylinder formula:

V=πr²h

V=π4²15

V=π16×15

V=240π

Then, you need to find the mass of the statue.

Mass:

Mass= density × volume

Mass=20×240π

Mass=4800π

Now, you need to find the volume. Since the sand has to weigh the same as the statue, the mass is going to stay the same. To find the volume you need to do:

V=mass of sand/density

V=4800π/2.5

That gives you your answer:

1920π

Note: I had to do the exact same problem on Khan Academy. This is right.