How fast is the volume of a sphere increases as the radius increases?
Since time just increases, and the radius increases as a function of time, and the volume increases as a function of a constant times the radius cubed, the volume increases faster than the radius increases, so we can’t just say the two rates are the same.
How fast is the volume changing when the radius is?
The average rate of change of volume with respect to radius as the radius of a sphere goes from 1 foot to 1.25 feet is 15.96 cubic feet per foot. 12.57 cubic feet per foot. For the large hot air balloon with radius r1 = 20 feet, the change in volume that is required for a three-inch increase in radius is much greater.
How fast is the volume of the sphere increases when the radius increases?
The rate of change of the radius dr/dt = . 75 in/min because the radius is increasing with respect to time. hence, the volume is increasing at a rate of 75π cu in/min when the radius has a length of 5 inches.
How fast is the area changing with respect to the radius when the radius is 120 cm?
What you calculated is the average rate of change of area between radii of 100 and 120 cm, not the instantaneous rate at 120 cm. To solve this problem, note that ddrπr2 (derivative of the circle’s area with respect to its radius) is 2πr, and substituting r=120 yields the correct answer of 240π.
What is the average rate of change of volume with respect to time from 0 min to 60 min?
Therefore, the instantaneous rate of change of volume with respect to time after exactly 60 min is about -13.3 L/min.
How do you represent a slope?
The slope is defined a s the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run. The slope of a line is usually represented by the letter m. (x1, y1) represents the first point whereas (x2, y2) represents the second point.
What letter represents Y-intercept?
In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis).