Until now, we have worked with two-dimensional fi gures; that is, we have worked with fi gures in a fl at plane, such as rectangles and triangles. A rectangle, for example, has the two dimensions of length and width. 1 Find the Volume of a Rectangular Solid In this section, we will learn about three-dimensional (or solid) objects like a rectangular solid and a pyramid. (A rectangular solid, or a box, has the three dimensions of length, width, and height.) We have found the area of two-dimensional fi gures, and now we will fi nd the volume of some three-dimensional objects. Definition The volume of a three-dimensional object is a measure of the amount of space occupied by the object or the amount of space inside the object. Volume is measured in cubic units. Here are two examples of cubic units used to measure volume. height 5 1 in. width 5 1 in. length 5 1 in. 1 cubic inch (1 in3) height 5 1 cm width 5 1 cm length 5 1 cm 1 cubic centimeter (1 cm3) If we say that the volume of this box is 18 cm3, it means that we can fi t 18 of the 1-cm3 boxes inside this larger box. Let’s begin fi nding volumes of solid objects (or solids) with a familiar shape: a box. A rectangular solid is a box-like shape with dimensions of length, width, and height. Volume 18 cm3 Formula Volume of a Rectangular Solid The volume, V, of a rectangular solid with length l, width w, and height h is Volume length width height or V lwh height, h width, w length, l Use cubic units to measure volume. Write a few sentences explaining the differences between area and volume. Include a statement about the units. www.mhhe.com/messersmith SECTION 4.4 Volume and Surface Area 319
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