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.
What is the formula to find the rate of change?
The rate of change can be depicted and calculated using the formula for rate of change, that is y2−y1x2−x1 y 2 − y 1 x 2 − x 1 , commonly known as slope formula.
How fast is the radius changing?
So, the radius is increasing at a rate of about 2.65 inches per minute when the radius measures 3 inches.
How do you find a spheres rate?
Assume that the radius r of a sphere is expanding at a rate of 7 in. /min. The volume of a sphere is V=43πr3 .
How do you find the rate at which the radius of a sphere is increasing?
We are also told the radius of the sphere is increasing at a rate of 2mm/s, so therefore dr/dt = 2mm/s .
How do you find the radius?
- When the diameter is known, the formula for the radius of a circle is: Radius = Diameter / 2.
- When the circumference is known, the formula for the radius is: Radius = Circumference / 2π
- When the area is known, the formula for the radius is: Radius = ⎷(Area of the circle / π)
What is the formula of volume?
| Table 3. Volume Formulas | Shape Formula Variables | Cube V=s3 s is the length of the side. | Right Rectangular Prism V=LWH L is the length, W is the width and H is the height. | Prism or Cylinder V=Ah A is the area of the base, h is the height. |
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How do you find the radius from the surface area?
Use the formula r = √(A/(4π)) . The surface area of a sphere is derived from the equation A = 4πr 2 . Solving for the r variable yields √(A/(4π)) = r, meaning that the radius of a sphere is equal to the square root of the surface area divided by 4π.
What is rate of change of volume?
The volume rate of change is the indicator that shows whether or not a volume trend is developing in either an up or down direction . ... If the volume today is higher than n-days (or weeks or months) ago, the rate of change will be a plus number. If volume is lower, the ROC will be minus number.
How do you find the rate of change of volume with respect to radius?
The Volume Rate-Of-Change indicator is calculated by dividing the amount that volume has changed over the last n-periods by the volume n-periods ago . The result is the percentage that the volume has changed in the last n-periods. If the volume is higher today than n-periods ago, the ROC will be a positive number.
The volume V of a sphere is four-thirds times pi times the radius cubed . The volume of a hemisphere is one-half the volume of the related sphere. Note : The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.
When the radius is 5 cm the radius is changing at a rate of?
When the radius is 5 cm, the radius is changing at a rate of cm/s . (Type an exact answer, using pi as needed.) b. When the circumference is 1 cm, the radius is changing at a rate of cm/s.
What is the rate of change of the area of a circle with respect to the radius?
Find the rate of change of the area of a circle per second with respect to its radius when radius=5cm. But the answer is 10π cm2/sec .
At what rate is the radius increasing?
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.
Is radius half of diameter?
The radius of a circle is the length of the line segment from the center of a circle to a point on the circumference of the circle and diameter is a line segment from one end of the circle to the other end of the circle passing through the center of the circle. So, the radius is half the length of the diameter .
