Sphere

A sphere is a three-dimensional geometric shape that is perfectly round, with all points on its surface equidistant from the center. It is a type of round ball shape, like a basketball or a globe.

Properties of a Sphere

1. Surface Area: The surface area of a sphere is given by the formula:

Surface Area = 4πr²

Where r is the radius of the sphere and π (pi) is a constant approximately equal to 3.14159.

2. Volume: The volume of a sphere is given by the formula:

Volume = (4/3)πr³

Where r is the radius of the sphere and π (pi) is a constant approximately equal to 3.14159.

Example Problems

1. Calculate the surface area and volume of a sphere with radius 5 cm.

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

Volume = (4/3)π(5)³ = (4/3)π(125) ≈ 523.6 cm³

2. Find the radius of a sphere with volume 288π cm³.

Volume = (4/3)πr³ = 288π

r³ = (3/4) * 288

r³ = 216

r ≈ 6 cm

Study Guide

When studying spheres, it's important to understand the concepts of radius, diameter, surface area, and volume. Practice calculating the surface area and volume of spheres using the formulas provided. Additionally, familiarize yourself with real-world examples of spheres, such as planets, bubbles, and sports balls, to appreciate the relevance of this geometric shape in the world around us.

Key concepts to remember:

• The radius of a sphere is the distance from the center to any point on the surface.
• The diameter of a sphere is twice the radius.
• The surface area of a sphere is 4πr².
• The volume of a sphere is (4/3)πr³.

By mastering these concepts and practicing related problems, you'll develop a strong understanding of spheres and their properties.