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Derivation (Proof) of Volume of a Sphere

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Explanations 1

Before we start, remember the Pythagorean Theorem: a2+b2=c2a^2+b^2=c^2a2+b2=c2 in a right triangle with legs a,ba,ba,b and hypotenuse ccc. We'll use this down below. Suppose tha…
By Sujay Kazi, HarryVector08, Victor Wang

Problems 4

A cube contains a sphere of volume 163π\frac{16}{3}\pi316π. What is the smallest possible volume of the cube?
A cube is inscribed in a sphere, which is inscribed in another cube. The side length of the larger cube is 10. What is the ratio of the volume of the sphere to the sum of the vo…
The volume of a sphere is 256256256 pi/3pi/3pi/3. Find the radius.
Bianca shoots a basketball with a radius of 12 cm. Padma hits a ping-pong ball with a radius of 2 cm. Sage kicks a soccer ball with a radius of 11 cm. What is the combined volum…