Question

the volume of a rectangular prism is 2.5 cubic feet. the prism has a height of 15 inches. what is the area, in square inches, of the base of the prism?
unit conversion table
1 ft³ = 1,728 in.³
1 ft² = 144 in.²
1 ft = 12 in.
type the number in the box.
square inches

Explanation:

Step1: Convert volume to cubic - inches

Since $1\ ft^{3}=1728\ in^{3}$, for a volume of $2.5\ ft^{3}$, we multiply by the conversion factor. So the volume $V = 2.5\times1728=4320\ in^{3}$.

Step2: Use the volume formula

The volume formula for a rectangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height. We know $V = 4320\ in^{3}$ and $h = 15\ in$. Rearranging the formula for $B$, we get $B=\frac{V}{h}$.

Step3: Calculate the base - area

Substitute $V = 4320\ in^{3}$ and $h = 15\ in$ into the formula $B=\frac{V}{h}$. So $B=\frac{4320}{15}=288\ in^{2}$.

Answer:

288