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If the radius of a cylinder is kept constant the derivative of cylinder volume is constant Why?
Wiki User
∙ 15y ago
Volume of cyliner=Pi(r2)h so if r is constant, the ony variable is h so what is dv/dh? Pi(r2) which is constant.
Wiki User
∙ 15y ago
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A hemi-spherical vessel has internal radius 0.5 m It is initially empty Water flows in at a constant rate of 1 liter per second Find an expression for the depth of the water after t seconds?
Since the vessel is hemispherical, its volume can be given by:V=((4/3)(pi)r3)/2V=(2/3)(pi)r3where r is the radius of the vessel.Since water is flowing into the vessel at a constant rate of 1 L/s, the volume of water in the vessel is thereby increasing at a constant rate of 1 L/s.By deriving the volume equation for the vessel with respect to time, we can equate the rate of change of the volume of water to the rate of change of the radius of the surface of water:dV/dt = (2/3)(pi)(3r2)(dr/dt)You must derive implicitly, so r3 derives down to 3r2(dr/dt) since the radius is also in itself a function of time. This equation can be cleaned up:dV/dt = 2(pi)r2(dr/dt)By solving for dr/dt, we get an expression for rate of change of the radius of the surface of water.dr/dt = (dV/dt)/(2(pi)r2)From the problem, we know that dV/dt is 1 L/s, and the radius of the hemisphere is a constant 0.5 m. We can substitute these known values into the equation:dr/dt = 1/(2(pi)(0.5)2)dr/dt = 2/piThis is the rate of change of the radius of the surface of water. The rate of change is a constant, which is important. Since it is constant, you can simply multiply this rate of change by a quantity of time to find the radius of the water level at any specific time. This is analogous to multiplying a constant velocity times a quantity of time to know an object's position at that time (a rate of change times an amount of change). We know that the vessel has an overall radius of 0.5 m, so the radius of the surface of water cannot exceed 0.5m.(dr/dt)= 2/pitherefore, depth at time t, D= 2t/piThis model gives the depth of the water (D) at any given time (t). As t increases, D(t) will return larger and larger values, which is expected since the water depth will increase as more water flows in.
How do you find the volume of a bolt?
measure it in a graduated cylinder
What is the second derivative of volume?
Derivatives are usually taken with respect to time. The first derivative would have units of volume / time, i.e., a flow - for example - "so-and-so many cubic meters per second flow down our river".The second derivate would refer to a change in the flow - when the flow of a liquid or gas increases or decreases with time.
How do you find the volume of a steel bolt?
Measure it in a graduated cylinder by seeing how much water it displaces.
A box is to have a square base an open top and volume of 2ft Find the dimensions of the box to the nearest inch that uses the least amount of material?
Let the length of the square be x and the height of the box be h. The volume of the box is the x2h=2ft2 The surface area (remember the top is open) is x2+4xh Using the first equation, make h the subject of the formula. h=2/(x2) and substitute this into the surface area formula. We then have SA=x2+8/x We have a minimum materials used when the derivative of this equation is equal to 0 SA'(derivative)=2x-8/(x2)=0 2x=8/(x2) 2x3=8 x3=4 x=1.59 ft h=2/x2=0.79 So the dimensions are 1.59 x 1.59 x 0.79 (2 dec pl.)
The volume of a circular cylinder varies directly with the height of the cylinder and with the square of the cylinder's radius If the height is halved and the radius is doubled then the volume will be?
The volume of a circular cylinder varies directly with the height of the cylinder and with the square of the cylinder's radius If the height is halved and the radius is doubled then the volume will be increased.
What is the volume of a cylinder with a radius of 3.5 and the volume of 5?
If the volume of the cylinder is 5, then its volume is 5 and its radius doesn't matter.
What is volume cylinder of radius 4cm and height 2cm?
A cylinder with a radius of 4cm and a height of 2cm has a volume of 100.53cm3
What is the volume of a cylinder that has a radius of 3cm and a height of 7cm?
The volume of a cylinder that has a radius of 3cm and a height of 7cm is 197.92cm3
What is the radius of a cylinder when the volume is 2500 and the height 16?
The radius of this cylinder is 7.0525.
How do you find the volume of a cone that fits exactly inside a cylinder?
volume=pi*radius squared*height/3, where radius is the radius of the cylinder (and will be the radius of the base of the cone),and height is the lenth of the cylinder.
How does doubling the radius of a cylinder affect the volume?
Doubling the radius quadruples the volume.
Volume of a cylinder?
Pi * Radius * Radius * Height.
How do you find the height and radius of cylinder with only the volume?
The volume of a cylinder is (pi)r^2h. This means the volume is dependent on both the height and the radius of the cylinder. So, one must know Volume and either radius or height to calculate height or radius respectively.
What is the volume of 10 in of an cylinder?
Volume of a cylinder = pi*radius squared*height
What is the height of a cylinder with a radius of 7 and a volume of 150?
The height of a cylinder with a radius of 7 and a volume of 150 is: 0.9744 units.
What is the volume of a cylinder that has a radius of 6 and a height of 8?
The volume of a cylinder that has a radius of 6 and a height of 8 is: 226.2 units3
