A pool in the shape of a rectangle prism is being filled with water. The length and width is 24 feet and 15 feet. If the hight o
f the pool is 1 1/3 feet, what is the volume of the water in cubic inches
1 answer:
Check the picture below.
![\textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=24\\ w=15\\ h=1\frac{1}{3} \end{cases}\implies V=(24)(15)(1\frac{1}{3})\implies \stackrel{in~ft^3}{V}=(24)(15)(\frac{4}{3}) \\\\\\ \stackrel{\textit{converting all feet to inches}}{\stackrel{in~in^3}{V}=(24\cdot 12)(15\cdot 12)(\frac{4}{3}\cdot 12)}\implies V=(288)(180)(16)\implies V=\stackrel{in^3}{829440}](https://tex.z-dn.net/?f=%5Ctextit%7Bvolume%20of%20a%20rectangular%20prism%7D%5C%5C%5C%5C%20V%3DLwh~~%20%5Cbegin%7Bcases%7D%20L%3Dlength%5C%5C%20w%3Dwidth%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20L%3D24%5C%5C%20w%3D15%5C%5C%20h%3D1%5Cfrac%7B1%7D%7B3%7D%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%2824%29%2815%29%281%5Cfrac%7B1%7D%7B3%7D%29%5Cimplies%20%5Cstackrel%7Bin~ft%5E3%7D%7BV%7D%3D%2824%29%2815%29%28%5Cfrac%7B4%7D%7B3%7D%29%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bconverting%20all%20feet%20to%20inches%7D%7D%7B%5Cstackrel%7Bin~in%5E3%7D%7BV%7D%3D%2824%5Ccdot%2012%29%2815%5Ccdot%2012%29%28%5Cfrac%7B4%7D%7B3%7D%5Ccdot%2012%29%7D%5Cimplies%20V%3D%28288%29%28180%29%2816%29%5Cimplies%20V%3D%5Cstackrel%7Bin%5E3%7D%7B829440%7D)
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