Question

(a) one crate has a length of 3 ft, a width of 2 2/5 ft, and a height of 5 ft. find its volume. (b) the other crate has a volume of 33 ft³ and a base area of 16 1/2 ft². find its height.

Explanation:

Step1: Calculate the volume for part (a)

The formula for the volume \(V\) of a rectangular prism is \(V = l\times w\times h\).
Given \(l = 3\) ft, \(w=\frac{2}{5}\) ft, \(h = 5\) ft.
Substitute the values into the formula: \(V=3\times\frac{2}{5}\times5\).
First, calculate \(\frac{2}{5}\times5 = 2\).
Then, \(3\times2=6\) ft³.

Step2: Calculate the height for part (b)

The formula for the volume \(V\) of a prism is \(V=B\times h\), where \(B\) is the base - area and \(h\) is the height.
Given \(V = 33\) ft³ and \(B = 16\frac{1}{2}=\frac{33}{2}\) ft².
We need to solve for \(h\), so \(h=\frac{V}{B}\).
Substitute the values: \(h=\frac{33}{\frac{33}{2}}\).
Using the rule \(\frac{a}{\frac{b}{c}}=a\times\frac{c}{b}\), we have \(h = 33\times\frac{2}{33}=2\) ft.

Answer:

(a) \(6\) ft³; (b) \(2\) ft