1. (10 Points) Suppose a water processing plant uses a water tank in the shape of a circular cone. The tank has height $h$, and the circular base has radius $r$. Find the volume of the cone in terms of the constants $r$ and $h$. Hint: Try using similar triangles to find a function for the radius at each cross section.
Added by Harry F.
Close
Step 1
The cross sections of the cone are circles, and the radius of each circle varies depending on the height of the cross section. Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 83 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A water tank has the shape of an inverted circular cone with radius 2 ft and depth 8 ft. Water is leaking out of the tank at a rate of 2 ft³/min. Let h represent the depth of water in the tank at any time, t. Compute dh/dt when h = 3 ft. Hint: the volume of a cone is given by V = 1/3 πr²h.
Sri K.
Filling a Conical Tank Water is poured into a container in the shape of a right circular cone with radius 4 feet and height 16 feet. See the figure. Express the volume $V$ of the water in the cone as a function of the height $h$ of the water. [Hint: The volume $V$ of a cone of radius $r$ and height $h$ is $V=\frac{1}{3} \pi r^{2} h$.]
Functions and Their Graphs
Mathematical Models: Building Functions
Water fills a cone-shaped container at a rate of 6 cm³/sec. The container is shaped such that the height of the water equals the diameter. How fast is the height of the water changing when the depth is 4 cm? Include units in the final answer and do not round. The equation of the volume of a cone is V = 1/3 πr²h Answer the question: Which variable do you need to get rid of? V - the volume r - the radius h - the height / depth t - the time You don't need to remove a variable for this problem.
Ahmet Y.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD