Best Answer

( The volume of a sphere is (4/3)(pi)r3 ).

The short answer: because of calculus.

The long answer:

This can be seen by using calculus to derive the volume of a sphere from the formula from it's surface area. To do this, we imagine that the sphere is full of infinity thin spheres inside it (all centered at the big sphere's center), and add up the surface areas of all the spheres inside.

The formula for the surface area of a sphere is 4(pi)r2. Let's call R the radius of the big sphere we want to find the volume of. To find the volume of this sphere, we add up the surface areas of all the spheres whose radii range from 0 to R. This gives the following formula (where r is the radius of each little sphere):

0R∫ 4(pi)r2dr

The 4 and pi can be factored out giving:

4(pi) (0R∫r2dr)

Integrating gives:

4(pi) [r3/3]0R

This is where the three comes from. Finishing the evaluation of the integral gives:

4(pi)(R3/3 - 03/3) = 4(pi)(R3/3)

Which can be rewritten as

(4/3)pi(R3)

which is the formula for the volume of a sphere.

Q: Why is the volume of a sphere divided by 3?

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Volume is 4/3 x "pi" x r3 or 4(pi)r3 divided by 3. Volume=7234.56 when pi is 3.14

Volume of a sphere = 4pi*r^3 2r = d, so Volume of a sphere = 4pi*(4)^3 Volume = 256pi

Volume of a sphere = 4/3*pi*radius3

The volume of every sphere is 4/3(pi) x (radius)3 .So the volume of your particular sphere is 4/3(pi) x (19)3.

Volume of cube = (side length )3 Volume of a sphere = 4/3*pi*r3 Looks like the sphere by a long shot, but let's see. Volume cube = (4)3 64 === The sphere has more volume.

Related questions

The density of a sphere can be calculated by dividing the mass of the sphere by its volume. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere. By knowing the mass of the sphere and its volume, you can determine its density as mass divided by volume.

Volume is 4/3 x "pi" x r3 or 4(pi)r3 divided by 3. Volume=7234.56 when pi is 3.14

Volume=(4/3)π(radius of sphere)^3

Volume of a sphere = 4pi*r^3 2r = d, so Volume of a sphere = 4pi*(4)^3 Volume = 256pi

Volume of a sphere = 4/3 * pi * r3 Volume of a sphere = 4/3 * pi(6 in)3 = 905 cubic inches ============

The volume of a sphere is 4 / 3 * pi * r3

Volume of a sphere = 4/3*pi*radius3

The volume of a sphere is the amount of space it occupies. Given a sphere's radius, r, the volume is 4/3 ∏r3

The volume of every sphere is 4/3(pi) x (radius)3 .So the volume of your particular sphere is 4/3(pi) x (19)3.

Volume of cube = (side length )3 Volume of a sphere = 4/3*pi*r3 Looks like the sphere by a long shot, but let's see. Volume cube = (4)3 64 === The sphere has more volume.

use the formula 4/3*π*radius3 to find the volume of a sphere.

Volume of a sphere = 4pir3/3 = 14710.2 units3