Question

If the length of the pool is 14 1/2 feet, the width is 6 1/2 feet, and the depth is 6 1/2 feet, what is the volume of the pool? The book shows the answer as 612 5/8 please show work

Answer 1

now, we're making an assumption that's a rectangular prism pool, so the volume is simple the product of length and widh and height, which we have, let's convert them all to improper fractions.

`\stackrel{mixed}{14(1)/(2)}\implies \cfrac{14\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{29}{2}}~\hfill \stackrel{mixed}{6(1)/(2)} \implies \cfrac{6\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{length}{\cfrac{29}{2}}\cdot \stackrel{width}{\cfrac{13}{2}}\cdot \stackrel{depth}{\cfrac{13}{2}}\implies \cfrac{4901}{8} \\\\\\ \cfrac{4896+5}{8}\implies \cfrac{4896}{8}+\cfrac{5}{8}\implies 612+\cfrac{5}{8}\implies 612(5)/(8)`