the volume of a rectangular prism is 2.5 cubic feet. the prism has a height of 15 inches. what is the area…

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?\nunit conversion table\n1 ft³ = 1,728 in.³\n1 ft² = 144 in.²\n1 ft = 12 in.\ntype the number in the box.\nsquare inches

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?\nunit conversion table\n1 ft³ = 1,728 in.³\n1 ft² = 144 in.²\n1 ft = 12 in.\ntype the number in the box.\nsquare inches

Answer

Explanation:

Step1: Convert volume to cubic - inches

Since $1\ ft^{3}=1728\ in^{3}$, for a volume of $2.5\ ft^{3}$, we have $V = 2.5\times1728=4320\ in^{3}$.

Step2: Use the volume formula

The volume formula for a rectangular prism is $V = Bh$, where $B$ is the base - area and $h$ is the height. Given $h = 15$ inches and $V = 4320$ in$^{3}$. We can solve for $B$ by rearranging the formula to $B=\frac{V}{h}$.

Step3: Calculate the base - area

$B=\frac{4320}{15}=288$ square inches.

Answer:

288