# math

The height of a cylinder with a fixed radius of 10 cm is increasing at the rate of 0.5 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 30cm.

1. 👍 1
2. 👎 0
3. 👁 776
1. v = pi r^2 h = 100pi h
dv/dt = 100pi dh/dt

Now just plug in your numbers to get dv/dt.

Note that it does not matter what the height is. Since the cylinder has a constant radius, its volume is directly proportional to its height.

1. 👍 0
2. 👎 3
posted by Steve

## Similar Questions

1. ### calc

When the height of a cylinder is 12 cm and the radius is 4 cm, the circumference of the cylinder is increasing at a rate of pie/4 cm/m in, and the height of the cylinder is increasing four times faster than the radius. How fast is

asked by marrisa smith on November 30, 2016
2. ### calculus

The height of a cylinder with a fixed radius of 4 cm is increasing at the rate of 2 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 14cm.

asked by emma on April 13, 2015
3. ### calculus

The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 20cm.

asked by Anonymous on December 17, 2014
4. ### math

Inside a long empty cylinder with radius R = 25 cm is put a long solid cylinder with radius r = 10 cm such that the bases of the two cylinders are attached. Then water is poured in the remaining empty region of the first cylinder

asked by emy on February 22, 2015
5. ### calculus

The radius of the base of a right circular cylinder is r com and the height is 2r cm. Find the rate at which the surface area of the cylinder is increasing when the radius is 5 cm and the volume is increasing at 5pi cm/sec. Thank

asked by Krystal on May 6, 2012
1. ### Calculus

A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h 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

2. ### calculus

A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h 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

asked by mike on March 31, 2013
3. ### Math

A cylinder is inscribed in a cone as shown in the diagram below. The cone has a height of 8cm and a fixed radius of R cm. The cylinder has a radius of x cm and a height of h cm. Show that the volume of the cylinder is maximised

asked by Isabel on November 29, 2016
4. ### Calculus

1) If y = 2x3 - 4x and dx, dt equals 4 , find dy/ dt when x = 1. 2) The area A = πr^2 of a circular water ripple changes with the radius. At what rate does the area change with respect to the radius when r = 4ft? 3) A rectangular

asked by Deondre on October 2, 2017
5. ### math

This one is kinda hard. "A ballon in the shape of a cylinder with hemispherical ends of the same radius as that of the cylinder is shown. The ballon is being inflated at the rate of 261pi cubic centimeters per minute. At the

asked by greg on November 14, 2007

More Similar Questions