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Archimedes' discovery of the volume and surface area of a sphere laid foundational principles in geometry and calculus, influencing future mathematical research and applications. His formulas, which state that the volume of a sphere is two-thirds that of the cylinder surrounding it and that the surface area is proportional to the square of its radius, are crucial in fields such as physics, engineering, and astronomy. This work not only advanced mathematical understanding but also demonstrated the power of geometric reasoning and the concept of limits, which are essential in calculus. Archimedes' contributions continue to be relevant in various scientific and practical contexts today.
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Why was Archimedes important to the world?
Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cyclinder. He is known for his formulation of a hydrostatic principle (known as Archimedes' principle) and a device for raising water, still used in developing countries, known as the Archimedes screw.
How Archimedes found the formula for finding the volume of the sphere?
Volume of a sphere = 4/3*pi*radius3 and legend has it that Archimedes was having a bath when he discovered the formula
What was Archimedes discovery about sphere and cylinder?
He discovered the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is 4⁄3πr3 for the sphere, and 2πr3 for the cylinder. The surface area is 4πr2 for the sphere, and 6πr2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. The sphere has a volume and surface area two-thirds that of the cylinder. A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.
How did Archimedes discover how to find the volume of a sphere?
How? With his brain! That's how he answered it
Who introduced the formula of cylinder?
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.
What is the surface area of a sphere with a volume of 3500pi?
The surface area of a sphere with a volume of 3500pi is: 2,391 square units.
Which Hellenistic inventor and mathematician experiment with levers created machine for raising and transporting water and determine formulas for calculating the surface area and volume of a sphere?
The Hellenistic inventor and mathematician you are referring to is Archimedes of Syracuse. He is renowned for his experiments with levers and for inventing machines such as the Archimedes screw for raising and transporting water. Additionally, Archimedes made significant contributions to geometry, including formulas for calculating the surface area and volume of a sphere, which he derived through his work on the relationship between spheres and cylinders.
What is the process used by Archimedes to determine the volume of a sphere with equal weights?
THE Method of Equilibrium
Who discovered the formula of a sphere?
i did i did Setting aside the answers by the two clowns, consider that it is generally attributed to Archimedes.
Who discovered the volume of cylinder?
Archimedes. Archimedes published a work named "On the Sphere and Cylinder", where he proved the formulas for the surface area and volume of both spheres and cylinders. This is actually quite impressive, considering that he lacked the concept of calculus or limits to aid him. In calculus, the proof for the volume of a cylinder because trivial through integration by slicing.
Can the surface to volume ratio of a sphere be the same as a cube?
No. The surface to volume ratio of a sphere is always smaller than that of a cube. This is because the sphere has the smallest surface area compared to its volume, while the cube has the largest surface area compared to its volume.
Who was the Greek mathematician who found the volume of a sphere?
4/3 *PI* r3 The formula was first derived by Archimedes, who showed that the volume of a sphere is 2/3 that of a circumscribed cylinder.
