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( 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.
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∙ 10y ago
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What is the volume of the sphere with a radius of 12?
Volume is 4/3 x "pi" x r3 or 4(pi)r3 divided by 3. Volume=7234.56 when pi is 3.14
What is the volume of a sphere with the diameter of 8 feet?
Volume of a sphere = 4pi*r^3 2r = d, so Volume of a sphere = 4pi*(4)^3 Volume = 256pi
How to find the volume of a sphere?
Volume of a sphere = 4/3*pi*radius3
What is the volume of a sphere with the radius 19?
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.
Which has more volume a cube of side length 4 or a sphere with radius 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.
Density of a sphere?
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.
What is the volume of the sphere with a radius of 12?
Volume is 4/3 x "pi" x r3 or 4(pi)r3 divided by 3. Volume=7234.56 when pi is 3.14
Formula for volume of sphere?
Volume=(4/3)π(radius of sphere)^3
What is the volume of a sphere with the diameter of 8 feet?
Volume of a sphere = 4pi*r^3 2r = d, so Volume of a sphere = 4pi*(4)^3 Volume = 256pi
What is the volume of a sphere with a radius of 6 in?
Volume of a sphere = 4/3 * pi * r3 Volume of a sphere = 4/3 * pi(6 in)3 = 905 cubic inches ============
How do you find volume of a sphere?
The volume of a sphere is 4 / 3 * pi * r3
How to find the volume of a sphere?
Volume of a sphere = 4/3*pi*radius3
What is the volume or a sphere?
The volume of a sphere is the amount of space it occupies. Given a sphere's radius, r, the volume is 4/3 ∏r3
What is the volume of a sphere with the radius 19?
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.
Which has more volume a cube of side length 4 or a sphere with radius 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.
How do you find the volume of a sphere?
use the formula 4/3*π*radius3 to find the volume of a sphere.
What is the volume of a sphere with radius 15.2?
Volume of a sphere = 4pir3/3 = 14710.2 units3
