Sphere

A sphere is a three-dimensional geometric shape that is perfectly round, like a ball. It is defined as the set of all points in space that are a given distance (called the radius) from a given point (called the center).

Formulas

The following are important formulas related to spheres:

Surface Area: 4πr², where r is the radius of the sphere.
Volume: (4/3)πr³, where r is the radius of the sphere.

Surface Area of a Sphere

To find the surface area of a sphere, you can use the formula 4πr², where r is the radius of the sphere.

Volume of a Sphere

The volume of a sphere can be calculated using the formula (4/3)πr³, where r is the radius of the sphere.

Example Problems

Let's solve a couple of example problems to understand how to apply the formulas for surface area and volume of a sphere.

Example 1

Find the surface area and volume of a sphere with a radius of 5 units.

Surface Area = 4π * 5² = 4π * 25 = 100π square units

Volume = (4/3)π * 5³ = (4/3)π * 125 = 500π cubic units

Example 2

If the volume of a sphere is 288π cubic units, find its radius.

Volume = (4/3)πr³ = 288π

Now, solve for r: r³ = (3/4) * 288 = 216

r = 6 units

Summary

In summary, a sphere is a three-dimensional shape with a perfectly round surface. The formulas for its surface area and volume are 4πr² and (4/3)πr³ respectively, where r represents the radius of the sphere.