 # why is sphere volume formula ## 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