Question

The volume of a right circular cylinder is given by V= πr2h, where r is the...

  1. The volume of a right circular cylinder is given by V= πr2h, where r is the radius of its circular base and h is its height.

  1. Differentiate the volume formula with respect to t to determine an equation relating the rates of change dV/dt , dr/dt , dh/dt.  
  1. At a certain instant, the height is 6 inches and increasing at 1 in/sec and the radius is 10 inches and decreasing at 1 in/sec. How fast is the volume changing at that instant? Is the volume increasing or decreasing? How can you tell?
Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose the radius, height and volume of a right circular cylinder are denoted as r, h,...
Suppose the radius, height and volume of a right circular cylinder are denoted as r, h, and V . The radius and height of this cylinder are increasing as a function of time. If dr/dt = 2 and dV/dt = 10π when r = 1, h = 2, what is the value of dh/dt at this time?
The radius of a right circular cone is decreasing at a rate of 1.5cm/sec and the...
The radius of a right circular cone is decreasing at a rate of 1.5cm/sec and the height is increasing at a rate of 5cm/sec. At what rate is the volume changing when the height is 12cm and the radius 2cm? Leave your answer in terms of pi.
The radius of a circular cylinder is increasing at rate of 3 cm/s while the height...
The radius of a circular cylinder is increasing at rate of 3 cm/s while the height is decreasing at a rate of 4 cm/s. a.) How fast is the surface area of the cylinder changing when the radius is 11 cm and the height is 7 cm? (use A =2 pi r2 +2 pi rh ) b.) Based on your work and answer from part (a),is the surface area increasing or decreasing at the same moment in time? How do...
A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If...
A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If the silo is to have a volume of 516π ft3, determine the radius and height of the silo that requires the least amount of material to build. Hint: The volume of the silo is πr2h + A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If the silo is to have a volume of 516π ft3, determine the...
A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the...
A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 6.5. What are the dimensions of such a cylinder which has maximum volume? Asking for both radius and height.
A potter forms a piece of clay into a right circular cylinder. As she rolls it,...
A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height hh of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.4 centimeters per second. What is the rate at which the radius is changing when the radius is 4 centimeters and the height is 11 centimeters?
1.) A rock is thrown into a still pond. The circular ripples move outward from the...
1.) A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at a rate of 5 ft./min. Find the rate at which the area is changing at the instant the radius is 7 feet. when the radius is 7 feet, the area is changing at approximately __ Square feet per minute 2.) The radius of a spherical...
The volume of a cylinder can be computed as: v = π * r * r...
The volume of a cylinder can be computed as: v = π * r * r * h Write a C++ function that computes the volume of a cylinder given r and h. Assume that the calling function passes the values of r and h by value and v by reference, i.e. v is declared in calling function and is passed by reference. The function just updates the volume v declared in calling function. The function prototype is given by:...
Suppose water is leaking from a tank through a circular hole of area Ah at its...
Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cAh 2gh , where c (0 < c < 1) is an empirical constant. A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its...
At noon, ship A is 150 km west of ship B. Ship A is sailing east...
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast is the distance between the ships changing at 4:00 PM? Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT