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 volume of prism: □×□ = □ cubic units area of shaded base: □×□ = □ square units

Explanation:

Step1: Recall volume formula

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 $l = 6$, $w = 7$, $h = 5$.
$V=6\times7\times5$
$V = 210$ cubic units.

Step2: Find base - area formula

The area of the base of a rectangular - prism (a rectangle) is $A = l\times w$. For the shaded base with $l = 6$ and $w = 7$, $A=6\times7 = 42$ square units.

Step3: Recall volume formula using base - area

The volume of a prism can also be written as $V=A\times h$, where $A$ is the area of the base and $h$ is the height. Since $A = 42$ and $h = 5$, $V=42\times5=210$ cubic units.

Answer:

(a) Volume of prism: $6\times7\times5 = 210$ cubic units
(b) Area of shaded base: $6\times7 = 42$ square units
Volume of prism: $42\times5 = 210$ cubic units