Posts Tagged ‘area’
Tuesday, September 8th, 2009
How to Find the Surface Area of a Pyramid
Description
This video gives a specific example for how to find the surface area of a pyramid, and also provides one of the basic formulas. The problem is completely worked through in the video to raise students understanding of the subject matter.
Overview
The surface area is the area of each side, or face, of the shape added together. For a pyramid, this typically means the rectangle or square that is the base, and the four triangles that make up the sides of the pyramid. There are more complicated versions of a pyramid, ones that have different shapes on the bottom and a different number of triangles, but the most common shape to see is a simple pyramid. First, solve for the areas of the triangles. The area formula for a triangle is A = (1/2) * b * h. If the shape on the bottom is a square, all the triangles have the same area and you will only need to multiply your answer by 4. If the shape is a rectangle or a more complicated shape, it is entirely possible that the triangles have different areas, and you may want to solve for area more than once. Then you need to find the area of the base. Depending on what your base is there will be a different area formula. Once you have all the areas, add them together to get the surface area of your pyramid.
Tags: area, formula, Geometry, Math, pyramid, rectangle, surface, surface area, triangle
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Surface Area of a Cylinder
Description
This video explains how to find the volume of a cylinder. It shows the different parts of a cylinder and says what parts need to be used to find the surface area and why. Examples are provided in the video.
Overview
The surface area is the area of each side, or face, of the shape added together. A cylinder as three faces – the base, which has two faces of equal area, and the middle section of the cylinder, which is actually a rectangle that has been wrapped into a round shape. However, because not all the dimensions of the rectangle are typically given in a manner easy to understand, there is a formula that can be used to solve for the surface area of a cylinder.
SA = 2 * (pi * r^2) + (2 * pi * r) * h
The first part of the formula represents the area of the two circles that form the base. The second part of the formula represents the circumference of the base (which is equal to the width of the rectangle) and the height of the cylinder (which represents the length of the rectangle).
Tags: area, circle, cylinder, formula, Geometry, Math, rectangle, surface, surface area
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Surface Area of a Sphere
Description
This video gives a visual representation of the surface area of a sphere. It shows what part of the sphere you would use for the formula for surface, although it is displayed on a several 2D shapes rather than the 3D shape you need to calculate for.
Overview
The surface area is the area of each side, or face, of the shape added together. For a sphere, this is a rather difficult concept – the sphere is simply a circle in 3D, and only has one face. So there is a set formula for the surface area of a sphere. It can be expressed as:
SA = 4 * pi * r^2
Where pi is a number approximately equal to 3.14, and r is the radius of the sphere.
Tags: area, circle, formula, Geometry, Math, sphere, surface, surface area
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Surface Area of a Rectangular Prism
Description
This video displays how to find the surface area of a rectangular prism. The different parts of a rectangular prism are explained in detail. One sample problem is worked through in the video to show how to correctly apply the formula.
Overview
The surface area is the area of each side, or face, of the shape added together. Rectangular prisms have 6 sides, which consist of 3 pairs. This makes solving for a rectangular prism’s surface area a bit easier. In order to solve for the surface area, you need to solve for the area of each face seperately, first. All the faces of a rectangular prism are rectangles, so the area can be found using this formula: A = l * w. You only have to solve for this three times – the matching face (found exactly opposite of the one you solved for) will have the same area, so just multiply your result by 2. After doing this three times, add them all together. Your result is the surface area.
Tags: area, formula, Geometry, Math, prism, rectangle, rectangular prism, surface, surface area
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Volume of a Cube
Description
This is just a short video showing a visual display of the volue of a small cube, and a formula for that specific cube is expressed at the end. That formula can be used to derive the formulas for other cubes.
Overview
A cube is a common object – they are any 3D square object with sides all measuring equal length. This can expressed the same way as a cube, but is easier to solve.
V = l * w * h = s^3
The length, width, and height are all the same on a cube so you can simply “cube” the number, or put it the third power. This is also why we call putting things to the third power “cubing”.
Tags: area, cube, cubes, finding volume, Geometry, height, length, Math, side, square, volume, volume of a cube, width
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Volume of a Rectangular Prism
Description
This video explains what a rectangular prism is and then gives and explains the formula to find the volume of a rectangular prism. This video provides two sample problems with easy to understand steps and solutions.
Overview
A rectangular prism is really just a rectangle in 3D. The volume of a rectanglur prism can be expressed like this:
V = l * w * h
Where l is the length, w is the width, and h is the height. This differs from an area formula because in an area formula there is no height, only a length and width.
Tags: area, finding volume, Geometry, height, length, Math, prism, rectangle, rectangular prisms, volume, volume of a rectangular prism, width
Posted in Geometry | No Comments »
Tuesday, September 8th, 2009
How to Find the Volume of a Cone
Description
This video gives an easy visual demonstration of the differences in volumes of two different shapes – a cone and a cylinder. The video proves that the formula must be different, because even though the height and base are exactly the same the volume is definitely not the same.
Overview
A cone is a pyramid that has the base shape of a cylinder instead of a rectangular prism. The volume of a cone can be expressed as:
V = (1/3) * B * h
Where h is the height, and B is the area of the base – the area of the base is the area of a circle, and can be expressed as pi * r^2.
Tags: area, base, circle, cone, finding volume, Geometry, height, Math, pi, radius, volume, volume of a cone
Posted in Geometry | No Comments »
Friday, September 4th, 2009
How to Find the Volume of a Pyramid
Description
This video shows the formula for finding the volume of a pyramid and provides one example problem. Content is shown in an organized manner.
Overview
The volume of a pyramid requires you to know the area of the base of the pyramid and the height of the pyramid. The volume can be expressed as:
V = (1/3) * B * h
The variable B represents the base – it is capitalized because you need to find the area. The base of a pyramid is a rectangle or a square. The variable h stands for the height of the pyramid, the length from the base to the point at the top.
Tags: area, base, finding volume, Geometry, height, Math, pyramid, volume, volume of a pyramid
Posted in Geometry | No Comments »
Thursday, September 3rd, 2009
Parts and Equations of Circles
Description
This video explains all the different parts of the circle, with multiple picture examples. Everything is laid out in an easy to read format and the illustrations clearly show where on the circle each part is located.
Overview
Circles are very interesting shapes in the world of geometry. There are many different parts to a circle, and many different formulas. The most common formulas are the area and the circumference formula.
Area Formula: Area = pi * radius * radius = pi * radius^2
Circumference Formula: Circumference = pi * diameter = pi * 2 * radius
The area is the area inside a circle, and the circumference is the measurement of the outside of the circle. The diameter is the width of the circle, and the radius is half of the diameter. Pi is a number that is equal to approximately 3.14.
The other parts of a circle are the sector, chord, arc, tangent, and secant. These are lines that will not show up all the time and will not always need to be acknowledged, but they do exist on the circle.
Tags: arc, area, chord, circle, circumference, diameter, Geometry, Math, pi, radius, secant, sector, tangent
Posted in Geometry | No Comments »
Thursday, September 3rd, 2009
Finding the Area of Basic Shapes
Description
This video provides equation and picture examples for how to find the area of the basic shapes rectangles, triangles, and parallelograms. Step-by-step instructions and easy to understand explanations are provided for each problem.
Overview
Solving for the area is very simple – values for lengths and other variables needed for finding the area should be provided, and in other cases the answer will be given but another variable will be left blank. Each shape has a different formula for area. They are as follows:
Square/Rectangle: Area = length * width
Triangle: Area = (1/2) * base * height
Parallelogram: Area = base * height
Once you have both the formula and the values, just plug them into the appropriate place and solve.
Tags: area, basic shapes, Geometry, Math, parallelogram, rectangle, shapes, triangle
Posted in Geometry | No Comments »
