How do you find the rate of change of volume?
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How do you find the rate of change of volume?
The rate of change in volume is dV/dt. The question is asking for the rate that the side length is changing. That would be ds/dt. If we take the derivative of both sides of V = s^3 with respect to time, we get dV/dt = d/dt[s^3].
How do you find the volume of a revolving solid?
If the axis of revolution is the boundary of the plane region and the cross sections are taken perpendicular to the axis of revolution, then you use the disk method to find the volume of the solid. Because the cross section of a disk is a circle with area π r 2, the volume of each disk is its area times its thickness.
How do you find the rate of change of demand with respect to price?
Demand: Compute the rate of change of x (the demand) with respect to p (the price). p = ‘ 200 -x 2x for0 . This is an implicit expression for the rate of change of the demand with respest to the price of the items produced.
What is a cross-sectional area volume?
The volume by cross section method takes the area of all of the slices of the shape and adds them together to find the total volume. For two shapes, if the corresponding slices have the same area then the sum will be the same and the shapes will have the same volume.
How do you find the rate of change using a graph?
To learn how to find the rate of change on a graph when given two points on the graph, follow these steps:
- Find the coordinates of the given points.
- Find the difference between the output values.
- Find the difference between the input values.
- Calculate the ratio between the change in y to the change in x: ΔyΔx.
What is the rate of change of the volume of a ball with respect to the radius when the radius is r 2?
Thus, the rate of change of the volume of the sphere is 4 π r 2 .
What is rate of change of radius?
The rate of change of the radius dr/dt = . 75 in/min because the radius is increasing with respect to time. At r = 5 inches, you find that. hence, the volume is increasing at a rate of 75π cu in/min when the radius has a length of 5 inches.
What is A circular cross-section?
The cross-sectional area of a cylinder is equal to the area of a circle if cut parallel to the circular base. The cross-sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional object – such as a cylinder – is sliced perpendicular to some specified axis at a point.
