Question

a cubes edge lengths are each 5 inches. a rectangular prisms length and width are also 5 inches, but its height is 7\frac{1}{2} inches. how many cubic inches larger is the rectangular prism than the cube? cubic inches

Explanation:

Step1: Calculate cube volume

The volume formula for a cube is $V_{cube}=s^3$, where $s = 5$ inches. So $V_{cube}=5^3=5\times5\times5 = 125$ cubic - inches.

Step2: Calculate rectangular - prism volume

The volume formula for a rectangular prism is $V_{prism}=l\times w\times h$. Here, $l = 5$ inches, $w = 5$ inches, and $h=7\frac{1}{2}=\frac{15}{2}$ inches. So $V_{prism}=5\times5\times\frac{15}{2}=\frac{375}{2}=187.5$ cubic - inches.

Step3: Find the difference in volumes

Subtract the cube's volume from the rectangular prism's volume. $V = V_{prism}-V_{cube}=187.5 - 125=62.5$ cubic - inches.

Answer:

$62.5$