Tap to Read ➤

Batul Nafisa Baxamusa
Jun 3, 2019

Volume of a sphere can be calculated using a geometric formula. Read on to know more.

Sphere is derived from the Greek word '*sphaira*, which means globe or ball. It is a three dimensional shape that has no base, edge, vertex, or face. It is a round body that has all its points on the surface that are equidistant from the center.

It is a perfectly symmetrical shape that has distance '*r*' (radius) from the center. Its diameter is the maximum straight distance through it, that is twice the radius. You can calculate the volume of a sphere using a simple formula. The following explanation will help you know more about this problem.

Deriving the equation will help you understand the puzzle better. The formula was derived by Archimedes. He showed that the volume of a sphere is 2/3^{rd} of a circumscribed cylinder.

Today, integral calculus is used to sum the volumes of an infinite number of circular disks with infinitesimal thickness. These discs have an incremental volume of **δV** as the product of the cross sectional area of the disk *x*, and thickness *δx*. Therefore,

**δV ≈ πy**^{2} • δx

Do not get confused looking at the incremental values represented using the Greek sign of delta (δ). Since this three dimensional figure is made up of many circles, a part of that figure is represented in this form.

You will get the total value by the summation of all the incremental volumes:

**V ≈ ∑πy**^{2} • δx

When the δx approaches zero in the limit, the equation becomes:

**V = **_{x = 0}∫^{x = r} πy^{2} • dx

'∫' is the sign of integration, i.e., the addition of all terms.

When the δx approaches zero in the limit, the equation becomes:

'∫' is the sign of integration, i.e., the addition of all terms.

A right angled triangle at any given *x* will connect *x*, *y*, and *r* to the origin. This is because it will follow the Pythagorean theorem as follows:

**r**^{2} = x^{2} + y^{2}

Thus, when you substitute*y* with the function of *x* you get:

**V = **_{x = 0}∫^{x = r} π (r^{2} - x^{2}) dx

Therefore,

**V = π ( r**^{3} - r^{3}/ 3) = 2/3 πr^{3}

Thus, when you substitute

Therefore,

Therefore, the volume of the sphere equation thus derived is as follows:

**V = 4/3 πr**^{3}

Find the volume of a sphere with a radius 7.6 m and round your answer to two decimal places.

*Answer*

V = 4/3 πr^{3}

= 4/3 x 3.14159 x 7.6^{3}

= 4/3 x 3.14159 x 438.976

V =**1838.7 m**^{3}

V = 4/3 πr

= 4/3 x 3.14159 x 7.6

= 4/3 x 3.14159 x 438.976

V =

The first formula was calculated using radius. Volume is a three dimensional amount of space that is occupied by an object. In a sphere, the distance from one point on the surface to another point on the surface through the center is measured with the help of diameter. To find the volume using the diameter, follow the following equation.

You just need to remember the formula and put in the values you've got. Hope this post has proved to be useful to all you who are zapped with mathematics.