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 $l = 9$, $w = 8$ and $h = 3$.
$V=9\times8\times3$
$V = 216$ cubic units.

Step2: Find area of shaded base

The shaded base is a rectangle with length $l = 9$ and width $w = 8$. The area formula for a rectangle is $A=l\times w$. So $A = 9\times8=72$ square units.

Step3: Find volume using base - area formula

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 $A = 72$ and $h = 3$. So $V=72\times3 = 216$ cubic units.

Answer:

(a) Volume of prism: $9\times8\times3 = 216$ cubic units
(b) Area of shaded base: $9\times8 = 72$ square units
Volume of prism: $72\times3 = 216$ cubic units