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 length of 4\frac{1}{5} ft, a width of 3 ft, and a height of 5 ft. find its volume.
(b) the other container has a volume of 22\frac{1}{2} ft³ and a base area of 15 ft². find its height.

Explanation:

Step1: Convert mixed - number to improper fraction

The length $l = 4\frac{1}{5}=\frac{4\times5 + 1}{5}=\frac{21}{5}$ ft.

Step2: Use volume formula for rectangular prism

The volume formula of a rectangular prism is $V=l\times w\times h$. Substitute $l=\frac{21}{5}$ ft, $w = 3$ ft, and $h = 5$ ft into the formula. $V=\frac{21}{5}\times3\times5$.

Step3: Calculate the volume

$\frac{21}{5}\times3\times5=21\times3 = 63$ $ft^{3}$.

Step4: For part (b), use the volume formula $V = B\times h$

We know that $V = 22\frac{1}{2}=\frac{22\times2+1}{2}=\frac{45}{2}$ $ft^{3}$ and $B = 15$ $ft^{2}$. From $V = B\times h$, we can solve for $h$ by $h=\frac{V}{B}$.

Step5: Calculate the height

$h=\frac{\frac{45}{2}}{15}=\frac{45}{2}\times\frac{1}{15}=\frac{45}{30}=\frac{3}{2}=1.5$ ft.

Answer:

(a) $63$
(b) $1.5$