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, space, g, slash, c, m, start superscript, 3, end superscript. The density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm
3
2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. The gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m.
In terms of \piπpi, what is the mass of sand Indiana Jones needs to avoid triggering the mechanism?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
{80\pi}\text{ g}80π g80, pi, space, g

(Choice B)
B
{4000\pi}\text{ g}4000π g4000, pi, space, g

(Choice C)
C
{12000\pi}\text{ g}12000π g12000, pi, space, g

(Choice D)
D
{32000\pi}\text{ g}32000π g

Answer 1

Given :  golden statue to be replaced with a bag of sand of equal weight .  golden statue cylinder with height 25 cm & radius 8 cm. Density of gold and sand is given

To find : Weight  of Sand

Solution:

golden statue cylinder with height 25 cm & radius 8 cm m

Volume of cylinder = πr²h

= π * 8² * 25

= 1600 π cm³

Density of gold  20 g/cm³

Density = Mass /Volume

=> 20  = Mass / 1600π

=> Mass = 32000π  g

Mass of Golden statue = 32000π  g

Mass  of Sand Required = 32000π  g

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