Question

problems 1 - 2: determine the surface area and volume of each rectangular prism. 1. surface area: __ square units volume: cubic units 2. surface area: square units volume: __ cubic units

Explanation:

Step1: Recall surface - area and volume formulas

The surface - area formula of a rectangular prism is $SA = 2(lw+lh + wh)$ and the volume formula is $V=lwh$, where $l$ is the length, $w$ is the width, and $h$ is the height. Assume each small cube has a side - length of 1 unit.

For the first rectangular prism:

Let's assume the width $w = 1$ unit, the height $h = 1$ unit, and the length $l = 4$ units.

Step2: Calculate the surface area

$SA=2\times(4\times1 + 4\times1+1\times1)$
$=2\times(4 + 4 + 1)$
$=2\times9$
$ = 18$ square units

Step3: Calculate the volume

$V=4\times1\times1=4$ cubic units

For the second rectangular prism:

Let the width $w = 2$ units, the height $h = 1$ unit, and the length $l = 4$ units.

Step4: Calculate the surface area

$SA = 2\times(4\times2+4\times1 + 2\times1)$
$=2\times(8 + 4+2)$
$=2\times14$
$=28$ square units

Step5: Calculate the volume

$V=4\times2\times1 = 8$ cubic units

Answer:

1. Surface area: 18 square units, Volume: 4 cubic units
2. Surface area: 28 square units, Volume: 8 cubic units