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

The volume of the prism is \(2.5\) cubic feet. Using the conversion \(1\,\text{ft}^3 = 1728\,\text{in}^3\), we calculate the volume in cubic inches:
\(2.5\times1728 = 4320\,\text{in}^3\)

Step2: Recall the volume formula for a prism

The volume \(V\) of a rectangular prism is given by \(V = B\times h\), where \(B\) is the area of the base and \(h\) is the height. We need to solve for \(B\):
\(B=\frac{V}{h}\)

Step3: Substitute values and calculate

We know \(V = 4320\,\text{in}^3\) and \(h = 15\,\text{in}\). Substituting these into the formula:
\(B=\frac{4320}{15}=288\)

Answer:

288