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 Speedy's cage than Fluffy's cage?

Answer 1

Speedy's cage is 2 inches taller than Fluffy's cage. This was calculated by finding the heights of both cages using the volume formula for rectangular prisms and subtracting Fluffy's cage height from Speedy's.

Step-by-step explanation:

To find out how much taller Speedy's cage is than Fluffy's cage, we first need to calculate the height of each cage based on the given volumes and other dimensions. The volume of a rectangular prism is calculated by multiplying its length, width, and height. Therefore, the height (h) can be found by dividing the volume (V) by the product of length (L) and width (W), as given by the formula h = V / (L * W).

For Fluffy's cage:
Volume (V) = 4,340 cubic inches
Length (L) = 20 inches
Width (W) = 14 inches
Height (h) = V / (L * W) = 4,340 / (20 * 14) = 15.5 inches

For Speedy's cage:
Volume (V) = 5,250 cubic inches
Length (L) = 20 inches
Width (W) = 15 inches
Height (h) = V / (L * W) = 5,250 / (20 * 15) = 17.5 inches

Now, simply subtract the height of Fluffy's cage from the height of Speedy's cage to find how much taller Speedy's cage is:
Taller height = 17.5 inches - 15.5 inches = 2 inches

Answer 2

2.5 inches taller

Step-by-step explanation:

x cubic inches = width × height × length

height = (x ÷ width) ÷ length