Question

the figure below shows a rectangular prism. one base of the prism is shaded.
(a) write an expression to find the volume of the prism using its length, width, and height. then simplify.
volume of prism: □×□×□ = □ cubic units
(b) find the area of the shaded base. then, using the area of the shaded base, write an expression to find the volume of the prism and simplify.
area of shaded base: □×□ = □ square units
volume of prism: □×□ = □ cubic units

Explanation:

Step1: Recall volume formula for rectangular - prism

The volume formula for a rectangular prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height. Given $l = 9$, $w = 4$ and $h = 6$.
$9\times4\times6$

Step2: Calculate the product

$9\times4 = 36$, then $36\times6=216$.
$216$

Step3: Find area of the base

The base of the rectangular prism is a rectangle. The area of a rectangle is $A = l\times w$. For the base, $l = 9$ and $w = 4$.
$9\times4 = 36$

Step4: Use base - area to find volume

The volume of a prism can also be found using $V=A\times h$, where $A$ is the area of the base and $h$ is the height. Here $A = 36$ and $h = 6$.
$36\times6 = 216$

Answer:

(a) Volume of prism: $9\times4\times6 = 216$ cubic units
(b) Area of shaded base: $9\times4 = 36$ square units
Volume of prism: $36\times6 = 216$ cubic units