How is the surface area of a sphere related to its volume?
How is the surface area of a sphere related to its volume?
For a sphere, surface area is S= 4*Pi*R*R, where R is the radius of the sphere and Pi is 3.1415… The volume of a sphere is V= 4*Pi*R*R*R/3. So for a sphere, the ratio of surface area to volume is given by: S/V = 3/R.
What is the rate of change of the volume of a sphere with respect to the radius?
Starts here2:29Calculus Related Rates: Rate of Change of Volume of SphereYouTubeStart of suggested clipEnd of suggested clip38 second suggested clipWe can always find rate of change of volume with respect to radius and that is DV over D R. So DVMoreWe can always find rate of change of volume with respect to radius and that is DV over D R. So DV over D R is 4 by 3 pi.
Can you find the surface area of sphere in any other way?
To find the surface area of a sphere, use the equation 4πr2, where r stands for the radius, which you will multiply by itself to square it. Then, multiply the squared radius by 4. For example, if the radius is 5, it would be 25 times 4, which equals 100.
How do you find rate of change and volume?
To find the rate of change of volume you have to take the derivative of the volume function with respect to r. dV/dr = 4(pi)r^2. Let r = 2. dV/dr = 16(pi).
What is the rate of change of the volume of a sphere with respect to the radius when the radius is R 3 in?
The rate of change when r= 3 cm is about 113.1 cm³ per cm.
What will be the rate of change of volume of sphere?
The rate of change of volume and area of a sphere is defined as the change of volume (dv) and change of area (da) of a sphere with respect to time (dt). d v d A = d v d t d A d t = 4 r 8 = 2 .
What is the rate at which the radius of a sphere?
The radius of a sphere is increasing at a constant rate of 3cms^-1. Given that the radius of the sphere is 5cm find in terms of π the rates at which its surface area and volume are increasing. The surface area of the sphere is 4πr^2.
What is the volume of the sphere when its diameter is 80mm?
We were given that the figure’s radius is increasing at a rate of 4. Therefore, we know Now we simply need to plug these values into the differentiated equation we found in step three. So this tells us that the volume of the sphere is increasing at a rate of 25,600, or about 80,424.772 when its diameter is 80 mm.
How do I change the volume of a sphere in Excel?
Type in the function for the Volume of a sphere with the radius set to r(t). Right-click on the expression and choose Differentiate>t. The rate of change of volume is 25 cubic feet/minute.
How do you find the rate of change of volume?
Enter in the expression for the Volume of a sphere (with a radius that is a function of ) and then differentiate it to get the rate of change. Type in the function for the Volume of a sphere with the radius set to r(t). Right-click on the expression and choose Differentiate>t. The rate of change of volume is 25 cubic feet/minute.
