Question

wendy keeps her hamster, fluffy, in a cage shaped like a rectangular prism that is 20 inches long, 14 inches wide, and has a volume of 4,340 cubic inches. kenneth keeps his hamster, speedy, in a cage that is the same length, but is 15 inches wide and has a volume of 5,250 cubic inches. how much taller is speedys cage than fluffys cage? inches

Explanation:

Step1: Find Fluffy's cage height

The volume formula for a rectangular prism is $V = l\times w\times h$. For Fluffy's cage, we know $V = 4340$ cubic - inches, $l = 20$ inches, and $w = 14$ inches. We can solve for $h$ (height) by rearranging the formula to $h=\frac{V}{l\times w}$. So, $h_{Fluffy}=\frac{4340}{20\times14}=\frac{4340}{280}=15.5$ inches.

Step2: Find Speedy's cage height

For Speedy's cage, $V = 5250$ cubic - inches, $l = 20$ inches, and $w = 15$ inches. Using the formula $h=\frac{V}{l\times w}$, we get $h_{Speedy}=\frac{5250}{20\times15}=\frac{5250}{300}=17.5$ inches.

Step3: Find the height difference

To find how much taller Speedy's cage is than Fluffy's cage, we subtract Fluffy's cage height from Speedy's cage height. So, $h_{Speedy}-h_{Fluffy}=17.5 - 15.5 = 2$ inches.

Answer:

2