Question

A rectangular prism has a length of 2 1/4 feet, a width of 6 feet, and a height of 3 1/2 feet.

Answer 1

ANSWER

$Volume = 47\frac{1}{4} {ft}^{3}$

EXPLANATION

The formula for calculating the volume of a rectangular prism is

$Volume = l \times b \times h$

Where

$l = 2 \frac{1}{4} ft$

is the length of the rectangular box,

$w = 6ft$

is the width and

$h = 3 \frac{1}{2} ft$

is the height of the rectangular prism.

We plug in the given dimensions into the formula to get:

$Volume = 2 \frac{1}{4} \times 6 \times 3 \frac{1}{2}$

Convert the mixed numbers to improper fraction to get:

$Volume = \frac{9}{4} \times 6 \times \frac{7}{2}$

Multiply out to get

$Volume = \frac{189}{4} {ft}^{3}$

Or

$Volume = 47\frac{1}{4} {ft}^{3}$

Answer 2

For this case we have by definition, that the area of a rectangular prism is given by:

$V = A_ {b} * h$

Where:

$A_ {b}:$ is the area of the base

h: It's the height

Before finding$A_ {b}$we convert the mixed numbers to fractions:

length: $2 \frac {1} {4} = \frac {4 * 2 + 1} {4} = \frac {9} {4}$

width: 6

Height:$3 \frac {1} {2} = \frac {2 * 3 + 1} {2} = \frac {7} {2}$

So, we have to:$A_ {b} = \frac {9} {4} * 6 = \frac {54} {4} = 13.5$

Finally, the volume is given by:

$V = 13.5 * \frac {7} {2} =47.25\ ft ^ 3$

Answer:

$47.25 \ ft ^ 3$