Question

1. which of the following formulas does not represent finding the height of a rectangular prism with a volume of 200 in³, a length of 4 inches, and a width of 5 inches? a. 200 = (4)(5)(h) b. 200 = (20)(h) c. 200 = \frac{(4)(5)}{h} d. \frac{200}{20} = h

Explanation:

Step1: Recall volume formula

The volume $V$ of a rectangular prism is $V = l \times w \times h$, where $l$ = length, $w$ = width, $h$ = height.

Step2: Substitute given values

Given $V=200$, $l=4$, $w=5$, substitute:
$200 = 4 \times 5 \times h$ or $200=(20)(h)$ (matches Option A and B).

Step3: Rearrange to solve for $h$

Rearrange $200=20h$ to get $h=\frac{200}{20}$ (matches Option D).

Step4: Identify invalid formula

Option C rearranges to $200h=20$, which contradicts the correct volume relationship.

Answer:

C. $200 = \frac{(4)(5)}{h}$