## Saturday, June 14, 2014

### Rectangular Parallelepiped Problem, 10

Category: Solid Geometry

"Published in Vacaville, California, USA"

A solid concrete porch consists of 3 steps and a landing. The steps have a tread of 11 in., a rise of 7 in., and a length of ft.; the landing is 6 ft. by 7 ft. How much material was used in its construction? Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above Photo by Math Principles in Everyday Life

The first that we need to do is to divide the given figure into rectangular parallelepiped as follows Photo by Math Principles in Everyday Life

There are one large rectangular parallelepiped and 6 small rectangular parallelepiped in the given figure. Let's assume that the steps of a ladder have 6 small rectangular parallelepiped whose dimensions are all congruent to each other.

For the large rectangular parallelepiped which is the landing, the volume is

For the small rectangular parallelepiped which is the step of a ladder, the volume is

Therefore, the volume of a ladder which is the amount of a material used in its construction is equal to