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 $l = 7$, $w = 2$ and $h = 8$.
$V=7\times2\times8$
$V = 112$ cubic units

Step2: Find area of the base

The base is a rectangle. The area formula for a rectangle is $A=l\times w$. For the base with $l = 7$ and $w = 2$, $A = 7\times2=14$ square units.

Step3: Find volume using base - area formula

The volume formula using base - area $A$ and height $h$ is $V=A\times h$. Since $A = 14$ and $h = 8$, $V=14\times8 = 112$ cubic units.

Answer:

(a) Volume of prism: $7\times2\times8 = 112$ cubic units
(b) Area of shaded base: $7\times2=14$ square units
Volume of prism: $14\times8 = 112$ cubic units