Posted by **Sara** on Saturday, April 10, 2010 at 6:30pm.

Spherical lead shot are poured into a square tray, 10 centimeters on a side, until they completely cover the bottom. The shot are poured from the tray into a graduated cylinder, which they fill to the 20-cm3 mark. What is the diameter of a single shot? How many shot were in the tray? If the 20 cm3 of shot had a mass of 130 grams, what would be the mass of a single shot?

- Itroductory Physical Science -
**drwls**, Saturday, April 10, 2010 at 8:44pm
Let D be the diameter in cm. The number of shot in the tray is approximately 100/D^2. The equation is not accurate unless D<<10 cm. With a hexagonal arrangement of spheres, you can get about 119/D^2 speheres in. It depends upon how you arrange the spheres and how much loose space remains at the edges.

The same number fills the cylinder up to 20 cm^3. Calculate the number of spheres of diameter D that can occupy that volume with hexagonal close packing. According to a theorem of Gauss, 74% of the volume can be occupied by solid spheres, whose volume is pi*D^3/6, so the number of spheres also equals

0.74*20/(pi*D^3/6) = 28.3/D^3

28.3/D^3 = 100/D^2 ; therefore

D = 0.28 cm

You can complete the other questions with that information.

## Answer this Question

## Related Questions

- Physical Science - A quantity of water is poured into a graduated cylinder, ...
- physics - in Melbourne there used to be a huge shopping centre called "diamaru" ...
- Science - Ethanol (grain alcohol) has a density of 0.789 grams per centimeter ...
- Maths - a tray holds 2.3 liters of water when full (2300 cm3) Calculate the ...
- chemistry - To determine the approximate mass of a small spherical shot of ...
- Math - The bakery has a full tray of brownies. One customer comes in and buys 1/...
- Math - Sarah is lining a square tray with 1 inch square tiles. The side length ...
- chemistry - A student estimated the volume of a liquid in a beaker to be 300 mL...
- math - This is the Crailsheim water tower in Baden-Württemberg, Germany. Its ...
- Physics - Glycerin is poured into an open U-shaped tube until the height in both...