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: Find area of base formula

The base is a rectangle. Area of a rectangle is $A = l\times w$, where $l = 8$ and $w=3$. So $A=8\times3$.

Step2: Calculate area of base

$8\times3 = 24$ square units.

Step3: Find volume formula

Volume of a prism is $V=A\times h$, where $A$ is the area of the base and $h$ is the height. Here $A = 24$ (from step 2) and $h = 9$. So $V=24\times9$.

Step4: Calculate volume

$24\times9=216$ cubic units.

Answer:

(a) Area of shaded base: $8\times3 = 24$ square units
Volume of prism: $24\times9 = 216$ cubic units
(b) Area of shaded base: $8\times3 = 24$ square units
Volume of prism: $24\times9 = 216$ cubic units