Math Problem Statement

Introduction As we saw in the Warm-Up, the area of a plane figure is the amount of space, measured in square units, that is enclosed by that figure. For a rectangle, the area is found by multiplying the length by the width.

Now we want to extend our understanding of measurement to solids, which are three-dimensional figures. Let's examine a rectangular prism that has a base with the same dimensions as the rectangle from the Warm-Up.

rectangle with dimensions of 8 units long by 5 units wide, showing unit squares; rectangular prism 8 units long, 5 units wide, and 3 units high, with bottom face the same as the rectangle write me a pharagragh on this

Solution

In this lesson, we are extending the concept of area from two-dimensional figures to three-dimensional solids. Just as the area of a rectangle is determined by multiplying its length by its width, we can apply a similar approach to a rectangular prism. A rectangular prism is a three-dimensional figure with length, width, and height. In this case, the base of the rectangular prism is a rectangle that measures 8 units long and 5 units wide, just like the rectangle from the warm-up. The height of the prism adds a third dimension, which is 3 units. The volume of this rectangular prism can be found by multiplying the area of the base (8 units by 5 units) by the height (3 units), giving us the total space enclosed within the prism. This extension to three dimensions allows us to measure and understand the volume, or the amount of space inside solids.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of Solids
Rectangular Prism
Measurement

Formulas

Volume of rectangular prism = length × width × height

Theorems

Volume formula for a rectangular prism

Suitable Grade Level

Grades 4-6