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suppose each cube in this right rectangular prism is a 1/2-in unit cube

Suppose Each Cube In This Right Rectangular Prism Is A 12in Unit Cube class=

Sagot :

Answer:

The length of each cube is given below as

[tex]l=\frac{1}{2}in[/tex]

Concept:

To figure out the dimension of the prism, we will calculate the number of cubes to make the length,width and height and multiply by 1/2

To figure out the length of the prism,

we will multiply 1/2in by 5

[tex]\begin{gathered} l=\frac{1}{2}in\times5 \\ l=2.5in \end{gathered}[/tex]

To figure out the width of the prism,

we will multiply 1/2in by 4

[tex]\begin{gathered} w=\frac{1}{2}in\times4 \\ w=2in \end{gathered}[/tex]

To figure out the height of the prism,

we will multiply 1/2 in by 3

[tex]\begin{gathered} h=\frac{1}{2}in\times3 \\ h=\frac{3}{2}in=1.5in \end{gathered}[/tex]

Hence,

The dimensions of the prism are

Length = 2.5in

Width = 2in

Height = 1.5 in

2.5in by 2in by 1.5in

Part B:

To figure out the volume of the prism, we will use the formula below

[tex]\begin{gathered} V_{prism}=base\text{ area}\times height \\ V_{prism}=l\times w\times h \\ l=2.5in,w=2in,h=1.5in \end{gathered}[/tex]

By substituting the values, we will have

[tex]\begin{gathered} V_{pr\imaginaryI sm}=l\times w\times h \\ V_{pr\mathrm{i}sm}=2.5in\times2in\times1.5in \\ V_{pr\mathrm{i}sm}=7.5in^3 \end{gathered}[/tex]

Alternatively, we will calculate below by calculate the volume of each cube and then multiply by the total number of cubes

[tex]\begin{gathered} volume\text{ of each cube=} \\ =l^3=(\frac{1}{2})^3=\frac{1}{8}in^3 \\ The\text{ total number of cubes =} \\ =5\times4\times3 \\ =60cubes \\ Volume\text{ of the prism } \\ =\frac{1}{8}in^3\times60 \\ =7.5in^3 \end{gathered}[/tex]

Hence,

The volume of the prism is = 7.5in³

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