Surface Area | Homework Help

Posts Tagged ‘surface area’

Surface Area – Cones

Tuesday, September 8th, 2009

How to Find the Surface Area of a Cone

Description

This video gives a clear example on how to solve for the surface area of a cone. The formula is explained and a sample problem is solved in the video.

Overview

The surface area is the area of each side, or face, of the shape added together. Cones are a very tricky shape to calculate the surface area of, because there is something called a “slant height” that needs to be used. The formula for the surface area of a cone is:

SA = B + pi * r * l

B is the area of a base. The base of a cone is always a circle. r is the radius of the circle – the base. l is the slant height. Sometimes you are given the slant height, but not always. If the slant height is not given to you then you can use this formula to find it:

l = sqrt(r^2 + h^2)

h represents the regular height of the cone, as opposed to the slant height. This is actually the pythagorean theorem – you can form a right triangle with it if you draw a picture.

Tags: area, circle, cone, formula, Geometry, Math, surface, surface area
Posted in Geometry | No Comments »

Surface Area – Pyramids

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 »

Surface Area – Cylinders

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 »

Surface Area – Spheres

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 »

Surface Area – Rectangular Prisms

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 »