the figure below shows a rectangular prism. one base of the prism is shaded.\n(a) write an expression to…

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

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

Answer

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 $l = 8$, $w=7$ and $h = 3$. $V=8\times7\times3$ $V = 168$ cubic units

Step2: Find area of shaded base

The shaded base is a rectangle. The area formula for a rectangle is $A=l\times w$. For the base, $l = 8$ and $w = 7$. So $A=8\times7=56$ square units.

Step3: Find volume using base - area formula

The volume formula using base - area is $V=A\times h$, where $A$ is the area of the base and $h$ is the height. We found $A = 56$ and $h=3$. So $V=56\times3=168$ cubic units.

Answer:

(a) Volume of prism: $8\times7\times3 = 168$ cubic units (b) Area of shaded base: $8\times7=56$ square units Volume of prism: $56\times3 = 168$ cubic units