why is sphere volume formula

ByMaksim L.

Sep 10, 2022

What is a formula for the volume of a sphere?

The formula for the volume of a sphere is V = 4/3 ?r?. See the formula used in an example where we are given the diameter of the sphere. Created by Sal Khan and Monterey Institute for Technology and Education.

How is sphere formula formed?

The general formula for the volume of sphere in terms of its radius is given as V = (4/3) ? r3. Let’s say ‘d’ is its diameter, according to the definition of diameter, we have d = 2r. From this, we get the value of radius = (d/2).

Who created the formula for the volume of a sphere?

A spectacular landmark in the history of mathematics was the discovery by Archimedes (287-212 B.C.) that the volume of a solid sphere is two- thirds the volume of the smallest cylinder that surrounds it, and that the surface area of the sphere is also two-thirds the total surface area of the same cylinder.

Why does a sphere have 4 3 volume?

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 ?R3, the cone is a third that, so the hemisphere volume is 23?R3. Thus the sphere of radius R has volume 43?R3.

What is formula for volume?

Volume Formula Variables. Rectangular Solid or Cuboid. V = l ? w ? h. l = Length. w = Width.

Who came up with the volume?

The precision of volume measurements in the ancient period usually ranges between 10–50 mL (0.3–2 US fl oz; 0.4–2 imp fl oz). The earliest evidence of volume calculation came from ancient Egypt and Mesopotamia as mathematical problems, approximating volume of simple shapes such as cuboids, cylinders, frustum and cones.

When did Archimedes discover the volume of a sphere?

The volume of the sphere was proved by Archimedes in around 250 BCE. His proof appears as Proposition 33 in his On the Sphere and Cylinder.

Who discovered formula?

The way Archimedes found his formulas is both amazingly clever and shows him to be a mathematician of the first rank, far ahead of others of his time, doing mathematics within touching distance of integral calculus 1800 years before it was invented.

Why is a sphere 2/3 of a cylinder?

Multiple Choice: 2/3 because the volume of the cylinder times 2/3 equals the volume of the sphere. 3. Multiplying the volume of a cylinder by 2/3 will give you the volume of a sphere with the same radius.

Why is the volume of a cone 1 3?

Fill the cones with water and empty out one cone at a time. Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.

What is 4/3 times pi times radius cubed?

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.

How do you find the volume and area of a sphere?

  1. Volume of a sphere: V = (4/3)?r. …
  2. Circumference of a sphere: C = 2?r.
  3. Surface area of a sphere: A = 4?r.

Which is the formula for the volume of a sphere with diameter D?

The volume of a sphere (V) in terms of its radius (r) is V = (4/3) ? r3. If d is its diameter, we have d = 2r. From this, we get r = (d/2). Substituting this in the volume formula, the volume of a sphere in terms of diameter is V = (?d3)/6.

What is the volume and surface area of sphere?

Sphere Formulas
Surface Area of a Sphere A = 4 ? r2
Volume of a Sphere V = (4 ? 3) ? r3

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