{"id":9476,"date":"2020-12-18T09:14:42","date_gmt":"2020-12-18T03:44:42","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=9476"},"modified":"2020-12-18T09:42:24","modified_gmt":"2020-12-18T04:12:24","slug":"volume-surface-area","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/volume-surface-area\/","title":{"rendered":"Volume and Surface Area"},"content":{"rendered":"

Volume and Surface Area<\/strong><\/span><\/h2>\n

Volume<\/h3>\n

Volume<\/strong> is the amount of three-dimensional space an object occupies, in cubic units, within a container.
\nVolume and Unit Cubes:<\/strong>
\nVolume is measured in cubic units. Think in three-dimensions.
\nThe volume of an object can be represented by the number of unit cubes<\/strong> that can be placed within the object.
\n\"Volume
\nFor some figures, the unit cubes fit “nicely” into the object, while other objects hold fractional parts of a unit cube.
\nThe volume of this rectangular prism (“box”) is the total of the number of unit cubes it holds. There are a total of 16 unit cubes within the solid.
\n\"Volume
\nThe volume = 16 cubic units<\/strong><\/p>\n

Volume as Area times Depth:<\/strong>
\nWhile counting the number of unit cubes within the rectangular prism,
\na pattern can be seen that will help to determine the count of the cubes quickly.
\nPattern:<\/strong> Find the number of cubes seen in one face and multiply times the number of rows of that face, going to the back of the figure.
\n\"Volume
\nVolume = (cubes in face) \u2022 (rows going back)
\n= 8 \u2022 2 = 16 square units
\nPattern:<\/strong> A pattern similar to that shown above can be expressed using the term “area”. The number of cube faces seen in the face of the figure, comprise the area of the face of the figure. The new pattern is expressed as:
\n\"Volume
\nVolume = (area of face) \u2022 (depth of face)
\n= (4 \u2022 2) \u2022 2 = 16 square units<\/p>\n

This will be a popular strategy to determine the volume of many solids.
\nThis pattern utilizes a “limiting argument” with the area being a 2-dimensional cross section with no thickness. The thickness, however, can be theoretically considered very, very, very small so as not to affect calculations. These cross sections are stacked to the height of the figure, creating the formula V = B \u2022 h, with B the area of the base and h = height.
\n(In the example about consider the area of the face to be the base, and the depth to be the height; just tip it over.)<\/p>\n

Surface area<\/h3>\n

Surface area<\/strong> is the total area that the surface of a three-dimensional object occupies, in square units.<\/p>\n

Surface Area using a Net:<\/strong>
\nIf you cut apart this box and flatten out the pieces, you will get a shape similar to the one at the right, called a net.
\nSeveral options are possible.
\n\"Volume
\nThe advantage of examining the net is that you can see each of the faces of the figure, making computing the surface area easier.<\/p>\n

\"Volume
\nThe surface area of this rectangular prism will be the sum of areas of all six shapes in the net.
\nSurface Area = (2\u20222) + (2\u20224) + (2\u20224) + (2\u20224) + (2\u20224) + (2\u20222) = 40 square units.<\/p>\n

Working with different units:<\/strong><\/p>\n