Question

the volume of a rectangular prism is the product of its length, width, and height. the length of a rectangle prism is 5 feet more than three times its height. the width is 7 feet less than nine times its height. express the length and width in terms of the height h. the length is the width is write down the expanded form of the expression for the volume: (be sure to expand the volume expression)

Explanation:

Step1: Find the length in terms of height

The length is 5 feet more than three times its height. If height is \(h\), then length \(l = 3h+5\).

Step2: Find the width in terms of height

The width is 7 feet less than nine times its height. If height is \(h\), then width \(w=9h - 7\).

Step3: Find the volume formula

The volume of a rectangular prism \(V=l\times w\times h\). Substitute \(l = 3h + 5\) and \(w=9h-7\) into the formula:

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Answer:

The length is \(3h + 5\).
The width is \(9h-7\).
The expanded form of the volume expression is \(27h^{3}+24h^{2}-35h\).