Hello everyone! Today we start a new exercise. It is “On a construction site, gravel is delivered and poured into a conical pile. The diameter and height of the cone of gravel are changing …” Let’s refer to how do it below!

Question: On a construction site, gravel is delivered and poured into a conical pile. The diameter and height of the cone of gravel are changing …

We have the following question: On a construction site, gravel is delivered and poured into a conical pile. The diameter and height of the cone of gravel are changing in a way that the diameter is always 3 times the height. If the delivery truck is set to pour the gravel at a constant rate of 3 cubic feet per minute, how fast is the radius of the pile changing when the height is 4 feet? (V=1/3πr²h)

Answer

Here are the steps to solve the question:

Step 1: Calculate h

Step 2: Calculate V

Step 3: Substituting the number we have:

Step 4: The end result is:

Relevant knowledge

A cone (also known as a cone) is a 3-dimensional geometry with a base of a circle and a pointed top.

Since the cone is formed when a right triangle is rotated around the axis of one of its right angles, the altitude and base radius can be considered as the two right angles of the triangle, and the birth line as the hypotenuse.
Therefore, knowing the altitude and radius of the base, we can calculate the birth line using the formula:
l = r² + h²
Knowing the radius and birth line, we calculate the altitude according to the formula:
h=l² – r²
Knowing the altitude and the birth line, we calculate the base radius according to the formula:
r = l² – h²

Conclusion

The article has helped you handle the question “On a construction site, gravel is delivered and poured into a conical pile. The diameter and height of the cone of gravel are changing …”. Wishing you great success in your studies!