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Which formula of the sphere is the result for solving the derivative of the volume?

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Which formula of the sphere is the result for solving the derivative of the volume?

The change in the volume (dV) would be the surface area times the thickness of the change (dr). So: dV = (surface area)*dr. Thus, surface area = dV/dr = the derivative of Volume with respect to r.

What is the derivative of a volume?

This means that the Volume is the Integral of the Surface Area with respect to the radius. By the FTOC, the Surface Area is the derivative of the Volume. This same phenomenon extends to other dimensions, for example, area and perimeter.

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What is the formula used to calculate the volume of any sphere?

Thus, the dimensional formula of volume of the sphere is V=43πR3 V = 4 3 π R 3 cubic units.

How did Archimedes find the volume of a sphere?

Archimedes used an inscribed half-polygon in a semicircle, then rotated both to create a conglomerate of frustums in a sphere, of which he then determined the volume.

What is the relationship between the volume and surface area of a sphere?

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.

Why is it 4 3 for volume of a sphere?

Since the cylinder/cone and hemisphere have the same height, by Cavalieri’s Principle the volumes of the two are equal. The cylinder volume is πR3, the cone is a third that, so the hemisphere volume is 23πR3. Thus the sphere of radius R has volume 43πR3. Integration.

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How do you calculate the volume of a circle?

is the radius and is the height/length.

  1. V = A h.
  2. Since the area of a circle = π r 2 , then the formula for the volume of a cylinder is:
  3. V = π r 2 h.

What are the formulas for calculating the volume of spheres?

Write down the equation for calculating the volume of a sphere. This is the equation: V = ⁴⁄₃πr³.

  • Find the radius. If you’re given the radius,then you can move on to the next step.
  • Cube the radius. To cube the radius,simply multiply it by itself thrice,or raise it to the third power.
  • Multiply the cubed radius by 4/3.
  • Multiply the equation by π.

    • How do you calculate the volume of a sphere?

    To calculate the volume of a sphere, use the formula v = ⁴⁄₃πr³, where r is the radius of the sphere. If you don’t have the radius, you can find it by dividing the diameter by 2. Once you have the radius, plug it into the formula and solve to find the volume.

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    What is the formula for finding the volume of a sphere?

    The formula for finding the volume of a sphere is 4/3 * Pi * r*r*r, where r is the radius of the sphere. Now to compute the volume of a sphere you have to note down the radius of the sphere and substitute it in the above formula along with the other substitutions.

    Who discovered the formula for the volume of a sphere?

    The volume of a sphere is the amount of space enclosed by the sphere. The formula for volume of a sphere and was first discovered by Archimedes and is 4/3πr3. Compared to other shapes, a sphere has the smallest surface area for its volume.

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