$$\dfrac{4}{3}\pi(3.1)^3-\dfrac{4}{3}\pi (3)^3$$
The formula for calculating the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius of the sphere.
The volume of a sphere is directly proportional to the cube of its radius. This means that as the radius increases, the volume increases at a faster rate.
Apc.3.1.8 refers to the third section, first subsection, and eighth sub-subsection of the AP Calculus curriculum. It covers the topic of differentiating volumes of spheres and is relevant to understanding the relationship between the radius and volume of a sphere.
When the radius of a sphere is doubled, the volume increases by a factor of 8. This is because the volume is directly proportional to the cube of the radius.
The volume of a sphere is used in various real-world applications, such as calculating the volume of a water tank, determining the amount of air in a balloon, or estimating the amount of medication in a spherical pill. It is also used in physics and engineering for calculating the volume of objects such as planets, atoms, and molecules.