## Thursday, June 12, 2014

### Rectangular Parallelepiped Problem, 8

Category: Solid Geometry, Physics

"Published in Newark, California, USA"

A tank, open at the top, is made of sheet iron 1 in. thick. The internal dimensions of the tank are 4 ft. 8 in. long; 3 ft. 6 in. wide; 4 ft. 4 in. deep. Find the weight of the tank when empty, and find the weight when full of salt water. (Salt water weighs 64 lb. per cu. ft., and iron is 7.2 times as heavy as salt water).

Solution:

To illustrate the problem, it is better to draw the figure as follows Photo by Math Principles in Everyday Life

There are two rectangular parallelepiped in the figure, the outside dimensions and the inside dimensions. The volume of a tank that is made of sheet iron is equal to the difference of the two rectangular parallelepiped.

For the outside dimensions, the volume of a rectangular parallelepiped is

For the inside dimensions, the volume of a rectangular parallelepiped which is also the volume of a salt water is

Hence, the volume of a tank is

Therefore, the weight of the empty tank is

The weight of the salt water is

Therefore, the weight of a tank filled with salt water is