Answer:
Explanation:
Here, we want to get the maximum load supported
From the first part of the question, we have it that:
The maximum load g, varies jointly with the width w and the height h, and inversely as the length l between the supports
Mathematically, we have that as:
where k is the proportionality constant
Now, let us get the value of k
We substitute the first set of values as follows:
Now, using this value of k, we want to get the value of g
Mathematically, we have that as:
Answer:
The volume of this pyramid is 16 cm³.
Step-by-step explanation:
The volume of a solid pyramid can be given as:
,
where
Here's how to solve this problem with calculus without using the previous formula.
Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.
Refer to the sketch attached. Let the vertical distance from the vertice be cm.
As a result, the length of a side of the square will be
.
The area of the square will be
.
Integrate the area of the horizontal cross-section with respect to
.
In other words, the volume of this pyramid is 16 cubic centimeters.
