In this lesson, we’ll go over some of the basic formulas and rules in geometry, the study of shapes and space.
You’ll learn formulas to find the perimeter, area, volume, and surface area of twodimensional and threedimensional shapes.
Geometry
In its simplest form, geometry is the mathematical study of shapes and space. Geometry can deal with flat, twodimensional shapes, such as squares and circles, or threedimensional shapes with depth, such as cubes and spheres.Before diving into twodimensional and threedimensional shapes, consider the basic geometric objects that create these shapes: points, lines, line segments, rays, and planes.A point is represented by a dot and shows a location in space.
A line is a set of straight points that extends forever in both directions as depicted by arrows on both ends. Rays are lines that end on one side. Line segments end on both sides. Planes are surfaces that extend forever in all directions.
As an example, to find the surface area of a sphere with a radius of 3 feet, simply square the radius and multiply by 4 and by 3.
14. The surface area is 113.04 feet squared.Volume is the amount of a space an object takes up.
For a cube, this means finding the area of one square, and finding how much stuff can fit inside if this square is stacked the same number of times as the length (or width). So, when solving for a cube’s volume, the length of the side can be multiplied by itself three times because its length, width, and depth are equal.Volume has many real life uses because it calculates how much an object will hold. For example, you might use the volume of a cylinder to find out how much water your bottle will hold. Even further, you may use the volume of a rectangle to find out how much junk your moving truck can hold when you buy a new house.
The formula to find the volume of a rectangular prism is V = lwh. To find the volume of a sphere, use V = 4/3 * (pi * r^3). Here’s an example for finding the volume of a sphere with a radius of a sphere, with a radius of 3 m. Start by cubing the radius to get 27 m squared. Then, multiply 4/3 by pi and 27 to get a final answer of 113.04 m cubed.And finally, to calculate the volume of a cylinder, use the formula V = Bh.
(B = Area of the base)
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