Mitchell Farms wishes to install a grain silo with a height of 20-50 feet and a radius under 10, the grain silo must have a volume of 10,000 cubic feet. For a cylinder of height h and radius r, the volume is given by V(r,h) = pi * ( r^2) * h If we wanted to keep the height between 20 and 50 feet, what interval of radii would we choose? If we wanted to keep the radius under 10 feet, what interval of height would we choose? Can their desire be met? that is can you suggest a cylinder with a height that falls between 20 and 50 feet AND has a radius under 10. On either plot, sketch y=x (or r=h in this case). Mitchell farm has inquired about equal height and radius, does this exist? how would drawing the r=h in this case be helpful?
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Mitchell Farms wishes to install a grain silo with a height of 20-50 feet and a radius under 10, the grain silo must have a volume of 10,000 cubic feet. For a cylinder of height h and radius r, the volume is given by
V(r,h) = pi * ( r^2) * h
- If we wanted to keep the height between 20 and 50 feet, what interval of radii would we choose?
- If we wanted to keep the radius under 10 feet, what interval of height would we choose?
- Can their desire be met? that is can you suggest a cylinder with a height that falls between 20 and 50 feet AND has a radius under 10.
- On either plot, sketch y=x (or r=h in this case). Mitchell farm has inquired about equal height and radius, does this exist? how would drawing the r=h in this case be helpful?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
