Question

a company sells two storage containers with different dimensions. each container is shaped like a rectangular prism. use the given information to answer each part below.
(a) one container has a base area of ( 17\frac{1}{4}\text{ ft}^2 ) and a height of 4 ft. find its volume.
base area ( =17\frac{1}{4}\text{ ft}^2 )
volume ( =square\text{ ft}^3 )
(b) the other container has a volume of ( 22\frac{1}{2}\text{ ft}^3 ), a length of 5 ft, and a height of ( 1\frac{1}{2}\text{ ft} ). find its width.

Explanation:

Step1: Convert the mixed number to an improper fraction

For part (a), \(17\frac{1}{4}=\frac{17\times4 + 1}{4}=\frac{68+1}{4}=\frac{69}{4}\).
The formula for the volume \(V\) of a rectangular prism is \(V=\text{Base Area}\times h\). Here, the base area \(B = \frac{69}{4}\text{ ft}^2\) and \(h = 4\text{ ft}\).
So, \(V=\frac{69}{4}\times4\).

Step2: Calculate the volume

\(V=\frac{69\times4}{4}=69\text{ ft}^3\).

For part (b), first convert the mixed numbers to improper fractions. \(22\frac{1}{2}=\frac{22\times2+1}{2}=\frac{44 + 1}{2}=\frac{45}{2}\), \(1\frac{1}{2}=\frac{1\times2+1}{2}=\frac{3}{2}\).
The formula for the volume \(V\) of a rectangular prism is \(V = l\times w\times h\). We know \(V=\frac{45}{2}\text{ ft}^3\), \(l = 5\text{ ft}\), \(h=\frac{3}{2}\text{ ft}\).
We can solve for \(w\) using the formula \(w=\frac{V}{l\times h}\).
Substitute the values: \(l\times h=5\times\frac{3}{2}=\frac{15}{2}\).
Then \(w=\frac{\frac{45}{2}}{\frac{15}{2}}\).
Using the rule \(\frac{a/b}{c/d}=\frac{a\times d}{b\times c}\), we have \(w=\frac{45\times2}{2\times15}\).
Cancel out the common factors: \(w = 3\text{ ft}\).

Answer:

(a) \(69\)
(b) \(3\)