How do you find related rate volume?
The volume of a cone of radius r and height h is given by V = 1/3 pi r^2 h. If the radius and the height both increase at a constant rate of 1/2 cm per second, at what rate in cubic cm per sec, is the volume increasing when the height is 9 cm and the radius is 6 cm.
How do you solve related rates problems?
- Draw a picture of the physical situation. Don’t stare at a blank piece of paper; instead, sketch the situation for yourself.
- Write an equation that relates the quantities of interest.
- Take the derivative with respect to time of both sides of your equation.
- Solve for the quantity you’re after.
How do you find the maximum and minimum volume?
To find the maximum possible volume, add the greatest possible error to each measurement, then multiply. To find the minimum possible volume, subtract the greatest possible error from each measurement, then multiply.
How do you calculate the volume of a tray?
Multiply the three sides together. Remember, the equation for volume is V = length x width x height, so simply multiply all three sides together to get your volume. Be sure to include the units you used to measure with as well, so you don’t forget what your numbers mean.
How do you find the volume of a rectangular box?
The volume of a rectangular box can be calculated if you know its three dimensions: width, length and height. The formula is then volume box = width x length x height. Illustration below: Measuring the sides of a rectangular box or tank is easy.
How do you find the rate of change of volume?
The rate of change of the volume is the derivative of the volume with respect to time. So that is dV/dt. Thus we need the derivative of the left side of the volume function. So we take the derivative of both sides (whatever you do to one side of the equation you must do to the other): Now I simplify this using the product rule:
How do you calculate the volume of a shipping box?
Alternatively, the area of one side of a box might be given, and the height relative to that side. In that case just multiply the area by the height. For example, if the base of the box is 25 sq ft and the side of the box ortogonal to it is 4 feet long, then the box volume is 25 x 4 = 100 cu ft. Cubic Meter / Cubic Feet cargo calculations
What is the rate of change of volume in dv/dt?
Since the Height is always 7 inches, V = 7LW. The rate of change of the volume is the derivative of the volume with respect to time. So that is dV/dt.