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 (the radius) from a given point (the center).

Formulas for Sphere

Here are the key formulas for a sphere:

• 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, use the formula 4πr², where r is the radius of the sphere. Remember that π (pi) is approximately 3.14159.

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. Make sure to use the value of π as 3.14159 for most calculations.

Example Questions

Let's solve some example questions:

1. If the radius of a sphere is 5 cm, find its surface area and volume.

Surface Area: 4π(5)² = 4π(25) = 100π cm²

Volume: (4/3)π(5)³ = (4/3)π(125) = 500π/3 cm³

2. What is the surface area of a sphere with a radius of 8 meters?

Surface Area: 4π(8)² = 4π(64) = 256π m²

Practice using these formulas and solving problems to master the concept of spheres. Understanding spheres is important in various fields, including mathematics, engineering, and physics.