Calculating the Volume of a Sphere

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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.

Equation Derivation

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.

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

Therefore, the volume of the sphere equation thus derived is as follows: V = 4/3 πr 3

Example

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

Formula using Diameter

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.

V is equal to 3.14159 (pi) times the diameter d that is cubed by 6. Therefore, the formula can also be written in the following way, as diameter is twice the radius ( r ). V = (π • d^ 3)/6

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.