the figure below shows a rectangular prism. one base of the prism is shaded. (a) write an expression to find…
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
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 $l = 8$, $w = 3$ and $h = 9$. $V=8\times3\times9$ $V = 216$ cubic units.
Step2: Find area of the base
The base of the rectangular prism is a rectangle. The area formula for a rectangle is $A = l\times w$. For the shaded base with $l = 8$ and $w = 3$, $A=8\times3=24$ 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 $A = 24$ and $h = 9$, $V=24\times9 = 216$ cubic units.
Answer:
(a) Volume of prism: $8\times3\times9 = 216$ cubic units (b) Area of shaded base: $8\times3 = 24$ square units Volume of prism: $24\times9 = 216$ cubic units