For this case we have by definition, that the area of a rectangular prism is given by:
[tex]V = A_ {b} * h[/tex]
Where:
[tex]A_ {b}:[/tex] is the area of the base
h: It's the height
Before finding[tex]A_ {b}[/tex]we convert the mixed numbers to fractions:
length: [tex]2 \frac {1} {4} = \frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]
width: 6
Height:[tex]3 \frac {1} {2} = \frac {2 * 3 + 1} {2} = \frac {7} {2}[/tex]
So, we have to:[tex]A_ {b} = \frac {9} {4} * 6 = \frac {54} {4} = 13.5[/tex]
Finally, the volume is given by:
[tex]V = 13.5 * \frac {7} {2} =47.25\ ft ^ 3[/tex]
Answer:
[tex]47.25 \ ft ^ 3[/tex]
ANSWER
[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]
EXPLANATION
The formula for calculating the volume of a rectangular prism is
[tex]Volume = l \times b \times h[/tex]
Where
[tex]l = 2 \frac{1}{4} ft[/tex]
is the length of the rectangular box,
[tex]w = 6ft[/tex]
is the width and
[tex]h = 3 \frac{1}{2} ft[/tex]
is the height of the rectangular prism.
We plug in the given dimensions into the formula to get:
[tex]Volume = 2 \frac{1}{4} \times 6 \times 3 \frac{1}{2} [/tex]
Convert the mixed numbers to improper fraction to get:
[tex]Volume = \frac{9}{4} \times 6 \times \frac{7}{2} [/tex]
Multiply out to get
[tex]Volume = \frac{189}{4} {ft}^{3} [/tex]
Or
[tex]Volume = 47\frac{1}{4} {ft}^{3} [/tex]
