Question

understand volume
1 attend to precision find the dimensions of the right rectangular prism shown in the diagram. the unit cube represents a volume of 1 cubic inch.
2 use structure ji builds a right rectangular prism with 14 centimeter cubes in the bottom layer (no gaps/overlaps). if there are 8 layers, what is the volume?
find the volume in cubic units.
3 diagram of rectangular prism
4 diagram of rectangular prism
use the unit given. find the volume.
5 diagram of rectangular prism
6 diagram of rectangular prism

Explanation:

Problem 2 (Ji's rectangular prism volume)

Step1: Identify bottom layer cubes

The bottom layer has 14 centimeter cubes.

Step2: Identify number of layers

There are 8 layers.

Step3: Calculate volume

Volume of a rectangular prism (built with unit cubes) is the number of cubes in one layer multiplied by the number of layers. So, \( 14 \times 8 = 112 \) cubic centimeters.

Answer:

The volume of the right rectangular prism is 112 cubic centimeters.

General Note for Volume of Rectangular Prism with Unit Cubes

For a right rectangular prism made up of unit cubes (with side length 1 unit), the volume can be found by counting the number of unit cubes. If we know the number of cubes in one layer (let's call this \( n \)) and the number of layers (let's call this \( l \)), the volume \( V \) is given by \( V=n\times l \). Also, if we know the length (\( l \)), width (\( w \)), and height (\( h \)) of the prism (in terms of unit cube side lengths), the volume is \( V = l\times w\times h \) (since each dimension is the number of unit cubes along that edge, and multiplying them gives the total number of unit cubes, which is the volume in cubic units).

For example, if a prism has length 5 unit cubes, width 3 unit cubes, and height 4 unit cubes, the volume is \( 5\times3\times4 = 60 \) cubic units.